Where it came from
The project's own history page is specific about its origin. "In April of 2014 at a Toronto hackathon a project called 'Dark Market' was created. Amir Taaki lead a small team of developers to build a proof of concept for a decentralized marketplace." The entry won, and the team stopped there. Brian Hoffman asked whether they were continuing, found they were not, "liked the idea of a decentralized marketplace, but didn't like the sole focus on darknet markets, so he forked the project and renamed it OpenBazaar."
The GitHub organisation dates to 29 April 2014. A first test release came that September. In 2015 the core contributors founded a company, OB1, on a $1 million investment from Union Square Ventures and Andreessen Horowitz, and rebuilt the software. The first full release shipped in April 2016. A second round of $3 million followed in autumn 2016 and paid for version 2.0, which ran nodes over a modified IPFS network with Tor support.
What it actually was
Not a website. A program you ran. Listings lived on the seller's own node rather than being hosted by anyone, payments went directly between buyer and seller, and disputes used multi-signature escrow with a third party the two sides picked. There were no platform fees and nobody who could remove a store, because there was no operator to ask.
That last property is also the reason it was hard to keep alive. A market with no operator has no revenue, so the company maintaining it was paying for search, wallets and seed infrastructure that the design deliberately did not charge for.
How it ended
OB1 ran on donations from September 2020. On 4 January 2021 the project posted: "It is with heavy hearts that we announce that @OB1Company will be decommissioning most of the infrastructure powering important parts of OpenBazaar on January 15th. Our donation funds have been depleted and OB1 will no longer be able to sustain covering those costs." Users were told to withdraw funds from their OpenBazaar wallets before that date, and the post added that OB1 would support anyone who wanted to carry the work on without it.
The main repositories are archived. The openbazaar.org domain now shows only the words "openbazaar 3.0 - coming soon", and an unfinished Rust implementation sits in the same GitHub organisation. No legal entity has been established for the project itself, so the structure is left undocumented.