Did the people of the 18th and 19th centuries realize that they were living through the "Industrial Revolution" and understand the enormity of what was happening as it happened?

My main focus in my research is the British Victorian age, so that is what I will draw from. For the Victorians, not only were they aware of the massive changes going on around them, for many it was the defining characteristic of their age. Some heralded it, some cursed it, some saw it as inevitable. "Progress" was one of the watchwords of the era. In 1833, now Edward Bulwer Lytton (now remembered for having written what is called the worst first line of all time) wrote "Every age must be called an age of transition - the passing-on, as it were, from one state to another never ceases; but in our age the transition is visible." The tremendous changes in technology and lifestyle was accompanied by huge population shifts. Between 1801 and 1901, the population went from about 9 million to 41 million. London went from 1 million to 6.2 million.

I can't overstate just how different city life was from what people had experienced before, and the Victorians documented it widely. Compassion and shock at the deplorable conditions in the cities was widespread, and efforts to alleviate some of the suffering occurred throughout the century. City slums were unspeakably filthy (with open cesspools, vermin-infested, and covered in animal droppings), and immensely overcrowded. There were high levels of prostitution, dangerous both for sex workers and their clients because of violence and disease, including the dreaded syphilis. Alcoholism and neglect were rampant, to the point that some people called baby farmers made a living being paid to raise other people's babies. One thing about the Victorians is that not only did they recognize these things, they worked to stop them. Charity societies, led especially by middle-class women, brought both religion and alms to the slums, though this coincided with "slum tourism" of people from privileged classes being shown around the worst parts of London the way people visited zoos.

English physician John Snow was horrified by the death toll of cholera in London, and he recognized that contemporary science knew nothing about the source of the illness, so he took it on himself to take voluminous notes on who was dying where. This allowed him to pinpoint some of the sources of disease, even down to an individual communal water pump (he famously removed the handle of the Broad Street water pump to stop people using it). Unfortunately, the general scientific consensus at the time was that "bad air" (miasma) caused disease, and not much was done on a broader level. The Great Stink of 1858, when hot weather combined with the waste in the city and Thames, finally led to a massive overhaul of the waste water systems of the city, helmed by Sir Joseph Bazalgette, that created much of the modern London sewerage system and drastically lowered the incidents of disease. This might seem like a small story, but it shows three key things to understanding the Victorian attitude towards their own age: the rise in horrible conditions caused by changes, the recognition and study of these, and large-scale steps taken to address them.

In some ways, factories allowed for high levels of employment and a regular wage, causing unprecedented opportunities for women to be independent and have a steady income. I won't go into too much detail about this, but the effects of factory work on people also caused a lot of outrage and demands for change. Newspapers carried stories of children whose bodies were mutilated by the machines they worked around, such as steam-powered looms that children would have to crawl inside of to clean out discarded material even while the machine was running. Long hours and cramped conditions led to permanent disfigurement, such as twisted spines, stunted growth, and cardiovascular problems from breathing in particles. Labor reform and child labor laws were put in place to try to control this.

According to David Newsome in The Victorian World Picture, the Victorians were very much aware that they were living in an age of massive change in economics, politics, technology, religion, culture, and society. A series of Reform Acts through the 19th century extended the right to vote from just the most privileged to all adult men, transforming the political landscape. The overthrow of Napoleon at Waterloo meant that Britain was the unrivaled power in Europe, though the rise of first Russia and later a unified Germany later in the 19th century would come to challenge this. The British struggle with Russia, especially over influence in India, would define much of their foreign policy, including the Crimean War of 1853-1856. The widespread colonies gave Britain unprecedented global influence, and the abuses and famines of the colonies were news and topics of debate throughout Britain. The other poster briefly touched on Karl Marx, and it's worth emphasizing that Karl Marx and Friedrich Engels gained much of their experience upon which they founded their theories in Victorian London. Ideas of race, class, and gender were widely debated (largely, but not exclusively, by university-educated white men). Charles Darwin's theories caused a profound shock to traditional notions of what humanity is and its place in the universe, and a decline in traditional churchgoing religion also saw an upsurge in interest in reformism and spiritualism.

Perhaps no event quite captures the spirit of the early Victorian age like the Great Exhibition of 1851 in Hyde Park. The brainchild of Prince Albert, himself personally responsible for encouraging technology and trade in many ways, the exhibition was a combination of demonstrating the latest technologies and showing the vast range of products available through the trade steam power and naval domination allowed. Countries from all over the world sent products to be displayed, and the whole exhibition occurred under a huge ~~steel~~iron-and-glass structure enclosing even full-grown trees. Among the items exhibited were the electric telegraph, the first modern toilets, and the huge Koh-i-Noor diamond, symbolic of British domination of India. Demonstrating typically Victorian attitudes towards both making things available to everyone and separating the classes, some days the tickets were one shilling and others as much as five. If you could pay it, you could avoid rubbing elbows with the working classes, but other days you could come see the most cutting-edge technology and products from around the world for an affordable fee. It's worth quoting Prince Albert's words at the opening of the exhibition at length. Note not only his pride in technological changes but also in the continued separation of people into classes, one of the bedrocks of Victorian society:

I conceive it to be the duty of every educated person closely to watch and study the time in which he lives.... Nobody... who has paid any attention to the peculiar features of our present era, will doubt for a moment that we are living at a period of most wonderful transition, which tends rapidly to accomplish that great end, to which, indeed, all history points — the realisation of the unity of mankind. Not a unity which breaks down the limits and levels the peculiar characteristics of the different nations of the earth, but rather a unity, the result and product of those very national varieties and antagonistic qualities.

The distances which separated the different nations and parts of the globe are rapidly vanishing before the achievements of modern invention, and we can traverse them with incredible ease; ... thought is communicated with the rapidity, and even by the power, of lightning. On the other hand, the great principle of division of labour, which may be called the moving power of civilisation, is being extended to all branches of science, industry, and art.

... [W]hilst formerly discovery was wrapt in secrecy, the publicity of the present day causes that no sooner is a discovery or invention made than it is already improved upon and surpassed by competing efforts. The products of all quarters of the globe are placed at our disposal, and we have only to choose which is the best and the cheapest for our purposes...

So man is approaching a more complete fulfilment of that great and sacred mission which he has to perform in this world. His reason being created after the image of God, he has to use it to discover the laws by which the Almighty governs His creation, and, by making these laws his standard of action, to conquer nature to his use; himself a divine instrument.

I will close briefly by writing that, by the end of the century, the optimism and hunger for new technologies, new colonies, and new ideas that had marked the Great Exhibition had largely worn out. There is a parallel nostalgia for the past that can be found throughout the Victorian period, from the longing for idyllic nature to the love of history and stories of old, such as King Arthur, seen nowhere more than in the works of the poet Lord Tennyson. The sense that the period of greatness was coming to a close pervaded the 1880s and 1890s, when a series of economic depressions, the rise of Germany and Russia, and the setbacks and horror of the Boer Wars contributed to a sense that Britain was in decline. Some of this was expressed in the Decadent movement, as fashionable young people such as Oscar Wilde replaced the earnestness of the past with ironic detachment. To some degree, however, people still believed the British society in particular and humanity in general was progressing towards a better, brighter future. It has been said that, in many ways, the Victorian faith in progress was finally shattered in the trenches of First World War.

I hope that answered some of your question. Yes, this was a topic of massive public conversation and debate. If you have follow-up questions, I hope I can answer those, too!