For example, if someone says "I'm so hungry, I could eat a horse," you would be playing with semantics if you responded with "Horses are not edible, so that doesn't make sense." The intended meaning of the statement is that the person is very hungry, not that they are literally going to eat a horse.
Playing with semantics can be a useful way to clarify the meaning of a statement or to highlight inconsistencies. However, it can also be used to avoid discussing the real issue at hand, or to simply be difficult.