The website says it is "a distributed version control system."
Let's start with the idea of a version control system. It's exactly what it says - it's a way to store and manage various versions of something. This is extremely important in programming, because a project is going to be changed many, many times as you develop it, and it will frequently be useful to have access to more than the current version. It's also going to be changed by multiple people; there has to be some way to combine everyone's changes.
The simplest possible version control would be to simply back up your entire project now and then, and pass either these snapshots or patches around between various developers. Obviously you would start running into difficulties eventually with such a naive approach; that's where dedicated version control systems come in.
A version control system will keep track of all of your history in an intelligent way, and allow you to browse that history, seeing everything about the changes: what they were, who made them, and why. Slightly more complex, they'll often have some notion of branching (creating divergent lines of development, perhaps for multiple developers) and merging (bringing those branches back together). Most version control systems will provide a lot of higher-level functionality on top of all this too. Just for a single example, git has a tool called "bisect" which will let you do a binary search through your history to find when a particular bug was introduced. Neat stuff.
There are two broad classifications of version control: centralized and distributed. In a centralized system, there is one central repository. It contains all of the history of the project, and anyone who wants to interact with that history has to go through that central repository. A distributed system like git, on the other hand, gives everyone that history. Each developer will end up with a copy (called a clone, in git) of the repository, which is completely self-sufficient. There's no need to interact with a public central repository except as a practical matter, a way of publishing content for others to see. This makes it much simpler for multiple people to work on the same project at the same time, possibly without having internet access, and also gives each of those people the full power of the version control system within their own repository, instead of the limited public functionality of the central repository.
For a great qualitative read on how you'd end up with a system like git, starting from the basics of wanting to remember history, try the git parable.
For more general information on the topic, try wikipedia: revision control.