The check engine light and other warnings lights are they to make sure you know what is going on with your car. Some, like the CEL and TPMS lights might be a serious problem to the safety of the car. Others, like the coolant temperature light are lights that some have seen before but never knew what it meant.
A good place to see a rundown of all the warning lights on your dashboard that apply to your specific car is to check out the owner’s manual. It explaina them all in detail and what you need to do when one lights up.