Macbook Air "shut down because of a problem"… why?

First time macbook user…. so I am freaking out about this…

I recently purchased a Macbook Air 13 inch, for grad school. I got it after having too many issues with my old Dell.

Everything was running smooth until yesterday. I was sitting in class and while working on a group assignment, and not using my mac for about 15 minutes, it shut down. Not knowing what was going on, I ended up pressing the power button until the screen turned on again. It took me to the login screen, and after logging in a window popped up saying "mac shut down due to a problem" and a 60 second countdown began saying that if I pressed continue it would take me to my home screen. So that is what I did. After that, I noticed my downloads icon in my dock disappeared and my downloads were not popping up like they used to (that lithe bouncy ball that went to the downloads in the dock. I was able to recover the downloads folder… but that downloading still isn't working like it used to.

Today, everything was running smooth until the professor let us out for a break. I closed my mac and went out. I wasn't even gone 10 minutes. I come back, open my mac and the screen is black. Once again it "shut down because of a problem" and the countdown popped up again.

What does this mean, how do I find out what the problem is, and what do I do?

I have applecare so if I need to I will go and see what is wrong, but I would like to have a possible idea of what the issue might be.

Any advice and assistance is appreciated.