Is it true that when your engine light comes on, it has nothing to do with how the car/engine is performing?

Well, yes and no... It can mean there is an issue. Sometime it can be a major problem, in which case you will notice the cars performance (or it dies or won't start). But it can also mean that its time to change the oil :)

What kind of car is it? (year, make, model)

It's a 2001 Chevy Malibu, with a 3.1 V6 engine

The Check Engine Light (CEL) comes on when there's a problem affecting emissions. Most of the time, it indicates a problem with the engine and/or transmission. Anytime the CEL comes on, get the codes stored in the ECU's memory read right away. Many auto parts stores will do this for free.

(cant rep u again tx)

I agree, especially with a chevy.. typically emissions
More specifically - I'm putting $10 that's its an O2 sensor :)