Bazaar is a distributed revision control system. What does that really mean? A revision control system is a program that tracks how the source code of a program changes. It tracks what the specific change was, such as the addition of a new piece of code, as well as who made the change. It also allows a developer to roll back to a previous version or create a branch to try a new idea.
The second key piece about Bazaar is that it is distributed. Traditional revision control systems have a single place where the code is stored. Only certain people can access this place and change the code there. A distributed revision control system is different in that there is no single place for code storage. Each branch a developer is working on is equal, and they all take code from each other. This system is much like a number of equal merchants at a bazaar, hence the name.
Bazaar started out as a fork of the Arch distributed revision control system. (A fork means that the developers disagree on where to take the program, and they break into different groups to work toward each group's different goals.) However, Bazaar 2 was completely rewritten, as it was found that the current code did not work in the long term.