You've already received some great answers as linked by u/CptNoble, I did however want to expand on a few points. In particular, you ask 'what they do' and 'what they stand for'. These are particularly pertinent questions and ones that are arguably still up for debate amongst masons today. Another important point touched on by the answers from a year ago, is the murky nature of masonic historiography. A lot of early masonic history is difficult to uncover and based on reasoned assumptions. As masonry becomes more profound in the 18th and 19th centuries, heaps of conspiracy theories are thrown on to further muddy the waters.

You have already received a reference to the earliest tangible masonic activity in the 1600s. The most famous of these is a diary entry from English royalist politician Elias Ashmole in 1646 who records the fact he was made a freemason alongside a certain Colonel Mainwairing. From this, we can assume lodges were already in existence, and therefore such activity dates back further. As you can probably gather, Ashmole was not an actual stonemason, he was what we call a 'speculative' (as opposed to 'operative') mason, one who was searching for a path of knowledge within a lodge. This begs the question as to how did Freemasonry emerge from actual stonemason guilds? This is a difficult one due to the lack of varied historical evidence to work from. The most convincing argument originates from Robert Gould's 1883 History of Freemasonry which was further complemented by the now defunct Canonbury Masonic Research Centre in the mid-2000s. Up until 1536 in England, the biggest employer of stonemasons, and sponsors of their guilds, were the monasteries. Henry VIII ordered their dissolution and the need, purpose, and influence of guilds were greatly diminished and eventually broken up by the King. This soon led to the formation of private lodges that also admitted freemen of the cities (it is speculated this was down to a lack of actual stonemasons), the precedent for allowing 'speculative' masons to join.

What we do and what we stand for now start to come into play. The French Wars of Religion ending in 1598 caused a mass exodus of French Protestants, the Huguenots, to both the Netherlands and England. Their shared experience of persecution and the exposure to open discussion in the Dutch Republic carried an intellectual movement into England which promoted religious tolerance. As many integrated into these new found lodges, their openness to other faiths acted as a watershed moment for what lodges stood for in an era of often rigid theological policy.

By the time we get back to Ashmole's time in Freemasonry, lodges are growing in terms of membership and the type of elite they attract, Sir Christopher Wren, the architect of St Paul's Cathedral, and Isaac Newton being notable contemporaries. Lodges soon become incubators of discussion and relative openness allowing ideas to be bandied around more so than the outside world. As you can imagine, this is hugely extrapolated as we reach the Enlightenment period.

The Enlightenment and Freemasonry could be an entirely separate question/answer but I'd rather direct your attention to post-Napoleonic Europe. As French armies marched across the whole breadth of Europe, Pandora's Box was opened to the ideas of popular sovereignty and national liberalism. As you may know, such ideas were met with horror by the ancien regime of Europe and frequently met with repression. In response, you see such ideas coalescing in masonic lodges, of various different Grand Lodges, such as the Carbonari in Italy. Such bodies spread across Prussia, the Habsburg Empire, and even Imperial Russia. Although not entirely led by Freemasons, the Decembrist Revolt in 1825, in opposition to absolutist Imperialist rule, had many leaders who were influenced by liberal ideas germinated in lodges elsewhere in Europe and carried to the port city of St Petersburg.

However, in the context of today's masons, what do we stand for? It goes without saying masonry has an illustrious history but your original question in today's societal context deserves an answer. In the Western world, the impact of the two World Wars paved the way for a resurgence in masonry. It also stopped being purely the realm of the gentry and aristocracy as many demobilised soldiers joined lodges to keep their camaraderie alive. Although numbers have declined since the 1980s, this ethos is alive and well. Freemasonry is seen as a social activity for many with the opportunity to socialise and meet people you otherwise wouldn't have (I should add nepotism is in fact forbidden by most masonic oaths). On the other hand, as discussed above, masonry was an opportunity for men to discuss ideas, explore themselves, and seek knowledge. This more esoteric road doesn't necessarily compete with the social aspect but the latter is seen as an 'easier' way to promote Freemasonry.

To be slightly contrarian 'what they stand for' is sometimes entirely in the mind of the member. Some join for company, some join for a deep dive into human nature and themselves. Without emitting personal feelings and sentiments too much, either is fine providing the member believes in brotherly love, relief, and truth.

References:

Gould R, History of Freemasonry (London 1883)

Jacobs M, Living The Enlightenment: Freemasons and Politics (Oxford 1991)

Jacobs M, 'The Radical Enlightenment and Freemasonry: Where We Are Now', Revista de Estudios Históricos de la Masonería (2016)

The Masons are definitely an interesting topic, so I hope more can be said. In the meantime, u/indyobserver and u/__4LeafTayback wrote about about them here.

/u/redrighthand_ gave a really great history.

To answer you a bit more briefly: it's often said that "Freemasonry is peculiar system of morality, veiled in allegory and illustrated by symbols".

If the off chance that you were in a college fraternity or sorority, many of the things in those actually come from freemasonry in terms of the rituals and some of the lessons taught.

There are three degrees, each of which teaches symbolic lessons to the candidate/brother about ethics, morals, and just sort of about life and death and trying to be a better man. Once you're a third degree (Master Mason) you can attend any meeting at nearly any lodge world wide. Meetings can either be pure business meetings that resemble any club where you read the minutes, debate if you're going to use company X or company Y to repair the AC, set up a committee to plan some charity event, etc...they can be "masonic education" where a speaker will give some kind of lecture or presentation about the symbols and lessons of the core of freemasonry, or the meeting can be to confer one of the degrees on someone.

People call it a secret society, but it's more a "society with secrets". Really the only true secrets are particular words and grips (handshakes) that you can use to identify yourself, and even those are available online if you really want to find them, though without going through the degrees they don't mean much, AND you're just as likely to find something that isn't true and someone just made up.

Ultimately, it's a group that, in today's world, tries to teach men to be better through symbolism and brotherhood.