Cherry picking is a kind of trick some people use when they try to make their argument look stronger than it really is. To do this they carefully pick out only the facts, statistics or examples that fit the argument they are making, while leaving out any facts or examples that don't support their argument. It's called cherry picking because it's like going through a fruit bowl and only picking out the cherries that you want, while leaving the other fruit behind.
All of us do this sometimes, but when we do it in an argument it's not fair because it makes it look like our argument is stronger than it actually is.