The inception of the Archive started after the decline of LiveJournal as a fanfic hosting platform, especially the notorious Strikethrough '07 incident, where LiveJournal responded to threats from a group of trolls purporting to be online vigilantes hunting paedophilic content by deleting a large number of allegedly "objectionable", but in most cases entirely innocent, journals and communities without warning, which resulted in many fans losing the contents of their journals. (Particularly affecting Harry Potter fandom, due to assumptions that any sexually explicit fanworks set in the universe must be "child porn".) AO3 as a project of the Organization of Transformative Works was a response to this, and the goal of the 'archive of our own' is to ensure a safe archive that would not purge fanworks due to pressure either from Moral Guardians or aggressive copyright enforcers.
To give an indication of how young it is compared to the existing behemoth Fan Fiction Dot Net (which started in 1998), AO3 reached one million stories in total on February 15, 2014. The Harry Potter fandom on FFN had roughly 674,000 on its own on the same day.
The rise in popularity has been helped along by the rise of Tumblr as both sites share a similar fandom mentality and outlook, as well as by AO3 being the official hosting site or encouraged posting site for a few popular fanfic fests and events such as Yuletide. It also gained popularity when Fanfiction.net had a crackdown on Mature Content Fics in June 2013 (the last time that website did such a crackdown was back in 2002). AO3 is very popular because it allows users to view fics as one single document instead of the separated chapters and even download stories as HTML, EPUB, MOBI, and PDF files, making it great for people who want stories on the go.
It also has a much less restrictive Review system than Fanfiction.net—like LiveJournal or Reddit, it uses comments which may be edited and stacked on at your leisure, rather than having a single use for each chapter that can never be edited, replied to only privately.
Also notable is the "Kudos" system, which allows someone to say that they like the work without going to the trouble of a comment, but still better than another tick on the view count.
The impressive usability and lack of censorship on AO3 has led to a massive and devoted group of users. So devoted that, in 2019, the entire website was first nominated and then awarded the Hugo award for Best Related Work.  The Hugo award is considered by many to be the premier honor in science-fiction, so just being nominated was an impressive for a website built and staffed mostly by volunteers.
"Tropes Of Our Own":
- Adjustable Censorship: If you, as a reader, don't want to see certain content, archive warnings, ratings, or pairings, you can set the search to filter whatever you don't want to see from the results. It's one of the most comprehensive filtering systems of any fanfiction archive, making it easy to find whatever you're looking for even outside of triggering or sexual content, such as a specific pairing, characterization, or AU scenario.
- Alan Smithee: If authors want to disassociate themselves from a work but don't want to take it down, they can choose to orphan the work. All orphaned works are moved to "orphan_account".
- Arson, Murder, and Jaywalking: There are multiple statements in AO3's Terms of Service reiterating that the website isn't responsible for any content that harms, disturbs, or triggers the user, often rattling off a list of intense adjectives describing said content that always ends with "grammatically incorrect" or "badly spelled".Unless it violates some other policy, we will not remove Content for offensiveness, no matter how awful, repugnant, or badly spelled we may personally find that Content to be.
- Bannedin China: A literal example. As of February 2020, Archive of Our Own has apparently been banned in China. On 29 Feb, Archive staff responded to reports from Chinese users that the site was inaccessible. They said the matter had been investigated and the problem was not on their end. There have been some rumors that this was due to complaints by one of the actors in the Chinese drama, The Untamed, over the portrayals of his character in fandom, especially ones involving queer content. This makes the situation quite ironic if the rumors are true. The Untamed is adapted from a popular Boys Love web novel, Mo Dao Zu Shi.
- Bowdlerize: Averted. Unlike Fan Fiction Dot Net, the Archive has minimal content restrictions, allowing explicit sexual content.
- Content Warnings: The Archive has four primary content warning flags: "Graphic depictions of violence", "Rape/non-con", "Major character death", and "Underage". Authors can also choose to select "None of these warnings apply", indicating the story has no major content warnings, or "Choose not to use Archive warnings", indicating that they have chosen not to forewarn readers as to the content. Additional content warnings may also be provided in the tags.
- Fake Relationship: Nearly 20,000 of them.
- Full-Name Basis: The character tags for each story use that character's full name, nicknames and codenames included. For example, an Overwatch story might be tagged with "Angela 'Mercy' Ziegler" or "Jack 'Soldier:76' Morrison", or a Gravity Falls story might include "Jesús 'Soos' Alzamirano Ramirez".
- Porn with Plot and Porn Without Plot: Both tags on the site.
- Real-Person Fic: Unlike Fan Fiction Dot Net, these are allowed on the Archive.
- Script Fic: The same applies to these.
- Soulmate AU Fic: 32,000+ of them, sorted into subcategories based on whatever Red String of Fate is prevalent.