Interference Engines and 60k's

[Tauni]

My car:

1997 Talon with no real mods. Exhaust, but not Catback. Drive train... No clue? But its non-turbo, automatic.

Anyways, here's what I need to know.

I went into Checker (my boyfriend works there), I was getting stuff for an oil change when I remembered Kevin had reminded me about 60k's, which I had forgotten about. I'm not 100% sure whether or not the guy before me did them, and I bought the car with 66k. So i'm figuring I should probably go ahead and do them, just incase. So when I went to Checker and asked for a timing belt the stared at me like I was nuts. They told me the price but they also said it was deffinately NOT a good idea for me to do it myself because my car has what's called an Interference Engine. (Not that I know what that means) Apparently, if I do the timing belt wrong, and it jumps, I will ruin my engine.

So my qusetion(s) are:

1. What exactly is an interference engine?
2. Exactly how greatly does it affect me (in other words, how much of what the told me is true)?
3. Should I trust a shop enough to take it in?
4. What other things should I do as 60k precautionaries?