You know all those behaviors that drive you crazy? Running away, shouting out, whining, hitting, etc.? Replacement behaviors are what we wish our students would do instead...and they should serve the same function as the original behavior. So instead of running away to get your attention, we would want our students to ask us to play a game with them. Or instead of whining every time they want the iPad, we may teach the replacement behavior of having a student request in a non whiny tone "Can I have the iPad please?"
The key factor with this is being able to identify the challenging behavior as well as the function it serves (attention, escape, sensory, or access tangibles) and then the appropriate replacement behavior.
The tricky part is figuring out what the function of the behavior is...so many behaviors can look the same, but serve a different function for each person doing them. For instance, let's look at an example of a student who runs away.