Building off of and rearranging what I've previously written here and here ...
In the early twentieth century, the 1890s represented the most recent and therefore easily remembered part of the Victorian era. "Victorian" has come to mean a lot of things beyond "relating to the reign of Victoria, 1837-1901": broadly speaking, things that are recognizably not "modern". This started relatively soon after the end of the queen's reign, with those in the late 1910s and 1920s seeing themselves as part of a "post-Victorian" age that was starkly different from what had come before. Anti-victorianism has largely been studied in the context of early twentieth century writers like those of the Bloomsbury Group - Virginia Woolf, Vita Sackville-West, T. S. Eliot, et al. - who distinguished themselves or who were distinguished by others as being intentionally anti-Victorian, or whose pro-Victorian sentiments need to be examined beyond simply being considered conservatism. These writers generally came of age around the turn of the century, spent their childhoods in middle- or upper-class Victorian households, and went on to become an educated, elite group that conspicuously spurned the mores and standards of their parents' generation, which to them represented the whole of the Victorian era despite being a highly skewed view of the entire period and all of the people in it. This backlash coexisted, however, with a nostalgia for (depending on one's age) the period of one's childhood or one's parents' childhood. You can compare this to the modern view of the 1950s - to some people, that decade is a time of backward social views and overly restrictive clothing, and to others, it's a glorious haven of innocence and beauty.
Aesthetically, the 1890s represented a lot of things that wouldn't and possibly couldn't come back. The dominant mainstream decorative arts movement was Art Nouveau, characterized by shapes in wood, stone, metal, and textiles with sinuous curves and unexpected proportions; while only the affluent could afford seriously art nouveau pieces for their homes, influence from it could be found in more mundane, utilitarian furniture and advertising/object packaging for the masses. Even when avant-garde artists like the Impressionists or Post-Impressionists rejected straightforwardly representational art, they still created works that involved great attention to detail and were clearly representing something. Women's clothing during the day was enveloping, generally involving a high collar, sleeves with a varying degree of fullness, a firmly-shaped figure, and long skirts, typically stiffened a bit at the hem in order to stand out; among women who were in a position to wear evening dress, that followed the same general lines and was often ornate and very well-made.
By contrast, the following decades had a very different material culture. "Smooth, streamlined, and geometric" essentially describes Art Deco and related early-twentieth-century styles like Bauhaus or Wiener Werkstatte: with no relationship to Art Nouveau's organic forms, or to previous artistic movements, they were completely modern. More and more abstracted artistic styles like Fauvism, Cubism, and Surrealism looked senseless and undetailed to many viewers. Women's dress was more lightweight and flimsy, covering less of the body and worn over fewer and more flexible undergarments; ready-made dresses were more available and common than ever before, helping to bring in a standard of looser and less precise fit. From about 1915 to 1930, the fashionable female figure was a lightly-shaped tube, and even when a more shapely form came into vogue again, it didn't seem quite as emphatic as the corseted one. (I've written about views of the Victorian corset during this period here.)
So, aesthetically, these eras are pretty much opposites, just as the 1950s and today are. If someone didn't like the modern aesthetic, the clearest place for them to turn to find a "better" one (more to their traditionalist taste) was the 1890s.
As you can see, I've left quite a bit of room for someone to talk about politics and business!
I haven’t seen anyone here mention the great nation building period (in the sense of physical construction) that took place once the civil war ended. While the Louisiana Purchase took place in 1803, the mass exodus to the west didn’t really explode until after the war ended. Irish immigrants, who arrived in great numbers during 1845 to 1849, went west with large numbers of city dwellers whose sole experience prior to the war was the city they had arrived in. After the war, many, including freed slaves and black soldiers who had fought for the union saw the west as a kind of new eden (salt lake city was founded in 1847) where opportunities would be radical. Remember, the addition of the formerly Mexican territory in 1948 through into relief the Missouri compromise - would the west be slaveholding? The civil war settled that in the negative, and so many Hs reason to belief that racism might lessen there.
In the post civil war period, just 8 years later was a recession, and then in 1884 was The Great Panic, in which it is estimated 5% of all American factories and mines closed. Overall, however, this was a long period of national organization and reorganization, in which a hardworking uneducated person could carve out and hold a farm, business or estate and massively rise in class - and the economic upheavals even added to the chance of rising, as investors might be laid low by a ship lost or a folded bank. 1873-1896 is also called the Long Recession but it’s worth noting that the extraction based economy is a different kind of disaster than what we think of as 20th century paper collapses like the stock market crash of 1929.
The gold rush of 1848 was in California, but the Klondike gold rush was 1896-1899 - in which the western cities of Portland and Seattle exploded.
Militarily, American identity gained primarily Other enemies in the Indian Wars and, in 1898, a decisive victory against Spain which gained us Puerto Rico, Guam, the Philippines, and that same year Hawaii ‘voluntarily’ joined the union. This created national pride, shared identity for those on the side of colonialism while avoiding much of the bitterness that protracted military expense and death can cause ina population.
Many of those new territories (and the west in general) became difficult and entangled in the first decade of the 20th century militarily and economically, along with labor organization and unrest. Additionally, the recession of 1901 and again in 1907 which were marked by (surprise) monopolies and trusts which resulted in income inequality and an increasing service class. So the era of those looking back was filled with the beginning of 'modern' problems (the first serial killer! Wobblies! Chinese Immigrants! Skyscrapers! Worker Deaths! Electrical lighting! Car Accidents!) and the newness of the problems might have made the old problems seem quaint and more manageable.
TL:DR - as /u/chocolatepot mentions, the aesthetic of the 1890s was a kind of metaphor for the entire Victorian era, and that was really the 50 year period in which ‘the American Dream’ was born - that an individual could become king of HIS own castle (women couldn’t achieve that autonomy for awhile), and answer to no master through only the meritocracy of hard work and cunning.
Clarification: nostalgic in what way? are you talking about the era usually referred as Belle Époque?
Is this in regards to Europe, or in America?
I would say I'm interested in because I recently gained a fascination for monarchy and empires in general. In the 1890s most of the world was basically still ruled by kings and queens, yet technology was somewhat advanced enough to record and document events through the use of photography, and later, primitive film.