To exceed is to go beyond expectations, or to go too far. If you exceed the speed limit, you might get a speeding ticket.
Exceed and excess share the Latin root excedere meaning to "go beyond." An excess is too much of something, like the piles of candy after Halloween, and exceed means the action of going too far in a good or bad way. You exceed in school when you get straight A's. When Dr. Jekyll transforms into Mr. Hyde, he experiences "a grinding in the bones, deadly nausea, and a horror of the spirit that cannot be exceeded at the hour of birth or death." No thanks! It helps to remember that like speed, exceed ends with -eed.