When I go (walk or drive) past you, I will wave to you. Whey I am going by, passing by you, I will wave. Imagine you are on the sidewalk and one of your friends passes by in a car. He waves to you, so he waved when he went past you.

It can be a little more subtle. If someone thinks they are better than you at something (like English!) you might decide that you are going to study hard and do better than them. It would be said to a rival.

It means exactly what it says. Which part is difficult?