There's much speculation on what happened "before" the big bang, but it's all speculation; there's pretty much so no evidence of any sort to back it up, save mathematical modeling.
The big problem with conceptualizing the big bang, is you have to think about space itself expanding, which is problematic for most people. Things are getting farther apart in such a way that the only real explanation is for space itself to be expanding. Imagine you had a rubber sheet, and pulled on all the edges and corners at the same time. Things on the sheet would move apart from each other at a particular rate, which is what we observe when we look at distant galaxies. It's not because things are physically moving in space, it's because space itself is expanding. As to what space is expanding "into," there could be courses taught on the subject, and I'm not well enough versed in theoretical physics to give you a good enough answer.
Once you've wrapped your mind around the concept of space expanding, it's fairly easy to imagine space shrinking. You could say that we're looking back in time, and seeing the entire universe, and more importantly space itself, getting smaller and smaller.
Now, just imagine an ordinary box shrinking. It gets smaller and smaller as its length, width, and height get smaller. Eventually, it gets so small you can't see it. Looking at it mathematically, it seems simple to make a box with its length, width, and height zero. It just means the volume is now zero too. Once you've got your box with no width, length, or height, and no volume, you have the universe before the big bang.
Here's the hard part: take that volume of zero, and put stuff in it. A lot of stuff; the entire universe in fact. All condensed into...nothing; a volume of zero can only be described as zip, zero, zilch, nada, absolutely nothing. Then, let's just start that space growing, and suddenly, everything "comes into existence" in an infinitesimal point. That point, which is the entire universe, expands rapidly, and is still expanding to this day.
Now, as to what caused the big bang, as I said, there's a lot of speculation and not a lot of evidence. When we look into the night sky, we are looking back in time, and we can't see past the point where the entire universe was similar to the core of a star (there's not a lot of space, so everything is squished together). One thing we do know, however, is that the universe's expansion is accelerating. It's been hypothesized that there's some form of "dark energy" which causes this expansion; what exactly that is, though, we don't know. It's reasonable to assume, however, that dark energy had something to do with "why" the big bang happened. You've also got the string theorists, who've proposed some crazy idea about "super-strings" which are basically multi-dimensional planes which universes exist on, and when these super-strings collide, you get a big bang. I don't put too much stock with them, though.
Remember, the big bang isn't so much of an "explosion" as much as "space and time popping into existence, with everything in the universe already contained inside of it." Of course, if you want to know what "existence" is, you're going to have to talk to a metaphysicist. Also, asking what happened "before" the big bang is pointless, because time came into existence with the big bang, so there is no "before."
Honestly, though, I can't imagine your professor asking anything more of you other than "the universe started as an infinitesimal point, which expanded into the universe we know today." The big bang theory mostly describes what happened immediately after the big bang, not the bang itself. Unless you plan on being an cosmologist or a theoretical physicist, you don't need to worry about it. If you're taking Astronomy 101, just quote the book, and you'll be fine.