To execute means to carry out in full or perform. If you execute all the difficult steps of the dance perfectly, you will make your instructor proud.
Here’s what’s tricky about execute: the first thing you think of is being punished with death for criminal actions. Actually, it's more commonly used in the sense of “to carry out in full.” So don't be alarmed with visions of the hooded guy at the guillotine when someone congratulates you on a plan well executed. Think of the word executive to get a closer grasp of both the meaning and the context.