The expression or saying smart as a whip means that you're very smart.
The saying smart as a whip comes from the sharp crack of a whip so when someone is saying you're smart as a whip they are saying that you're very sharp and smart.
I could not see why smart as a whip was a saying until I researched it more because I thought that whips cannot be smart so how could someone be smart as a whip?
But it just has to do with the sharp crack of the whip meaning you're very smart and intelligent.
For example if a 3 year old boy is reading at a higher level than normal then he would be smart as a whip.