Refusing to leave a private property when ordered to do so is one form of trespassing. This occurs when a person who has no right to be on some piece of private property refuses to leave when ordered to do so by someone in authority.
Here is a situation in which this might happen. Let's say you are driving in the countryside and you see an old barn you would like to look at more closely. You stop and walk over to it. As you are looking, the owner of the land comes and asks you to leave. At that point, you are not trespassing if there were no signs up warning you that this was private property and that you should not enter. However, if you do not leave the property when the owner says to, you are guilty of trespassing through your refusal to leave.