My first game jam was Ludum Dare, and wow what a weekend. I remember being excited, nervous and slightly doubtful that I could produce much in 48 hours. I did it though, and I'm happy with what I managed to produce.
So what did I get out of it? Well for a start I got a completed game. It is difficult to get the motivation to complete a game at the best of times, so having a short deadline really worked well for me. I did not have long enough to get bored.
It also introduces you to a great big community out there. Seeing other people comment on my games, offering up good advice make you realise where you can push your skills further. It gives you another perspective on what you do.
The next question I get asked is where can I find these competitions?. A great place to start is compohub. You can see what is happening now, and in the next couple of months. You will also need to dig around for other events. The next event I am planning to enter I only found out about by talking to other developers. That event is the 0 hour game jam, which takes place in the hour the clocks go back.
In the future I would like to host a game jam myself. It will be for open source games, meaning that you can only use open source software. The results will also be open, so that over time competitions can build on the work done from previous rounds. Watch this space.