Git has caught the imagination of a very large number of people writing software, as well as many other people writing things they want to share, version and track. It's is a Distributed Version Control System, which means that anyone with the repository of files has the full respository and all history. No remote server needed.
Git's been very successful for a number of reasons.
Firstly, it's an excellent tool that works in a way many developers find natural in today's networked world : offline use, easy branching, good merging etc. It's also extremely fast.
It also has a very broad ecosystem built around it, not least Github, a very popular and sophisticated web-based front-end.
Perhaps one of the big reasons for its growing popularity is its constant good "press". People write about it a lot, and what they write is often of a very high quality. Guides, tips and tricks, workflows and diagrams, and free online books. Git discussion and comment has a very high signal to noise ratio. So there is a constant good buzz around it. This is the best advertisement possible.
Linus Torvalds has a pretty good track record now.
I have borrowed the nice little pictures here from Scott Chacon's Git Reset post. Scott's the author of the Pro Git book, available for free at the same place. This is a great example of the high quality Git ecosystem