The longer story is that myself and a couple of guys from Italy (Stefano and Pier) took over Apache JServ, which was the only open source servlet engine at the time. We started to make some significant improvements and created Apache Java as an umbrella project. Apache made us some of the first non-httpd members.
We eventually got noticed by James Davidson at Sun, who was working on the servlet API and the reference implementation of that. Eventually, we decided to merge our efforts. Sun didn't like us using the Java (tm) name, so we picked the name of the conference room that we had the discussions in. That turned into renaming everything Apache Jakarta. It also involved giving us their reference implementation, which we named Apache Tomcat. The build system for Tomcat (because nothing good existed at the time) ended up turning into Apache Ant.
After insane amounts of work, we grew quite a bit as an organization. One day, I saw Doug Cutting working on the Lucene project and invited him under the Jakarta umbrella. That led to things like Hadoop and that whole ecosystem.
Edit: To clarify the JServ stuff. I had a web development company at the time. I wanted to work in Java and all the servlet stuff at the time was commercial products that were not very good. I found JServ, which one guy had built as a college/parttime project and then abandoned it, full of bugs and not finished.
So, I picked it up and started to work on fixes and then Stefano/Pier somehow found me. At the time, Apache didn't even have a way to host this stuff, so I ran it under my own (working-dogs.com) domain for about a year or so.
Eventually, through his work at Apache, Brian Behlendorf figured out there was a business in hosting code... so he started CollabNet. I quit my company and went to work with him and a bunch of other Apache folks. That's where subversion was created and Github eventually won that competition.