For anyone unfamiliar, crit is short for critique. In classes and when submitting work to exhibitions, everyone has to hang their work up or hand it to someone else and say, "Here is what I did, here is what I tried to accomplish, tell me what you think." Sometimes entire groups of people critique your work, sometimes one person. Sometimes you're present, sometimes you aren't. The ultimate goal is to hear what people think of your execution, both technical and conceptual, and find out what is great and what you can improve on.
Even though crits can be nerve-wracking and scary, they're really important, and you should have them as often as possible. Talk to everyone about your work that is willing to have a conversation, and if possible, talk to established artists. Talk to your professors. I know I've had a great day when I have a one-on-one talk with Jon or Larry, and even better if I make it through without crying or making excuses.
If you have a visiting artist at your school or studio and you're graciously given the opportunity to have them look at work, take it. Always take it. I was lucky enough to be recommended to have a talk with Dan Torop (the only sophomore invited; a couple of juniors were asked, and the rest were seniors). I didn't know anything about Dan, but I said I would love the opportunity, and then I spent the next 24 hours freaking out about what I was going to show him. I was freaking out up until he walked in and we started talking, and then I was too busy having a conversation about art and learning about Dan and myself to be freaking out.
Always take good opportunities that will further your knowledge, no matter how scary and no matter how unprepared you think you are.