To complicate things is to make them more complex, confusing, or difficult. So if you've already accepted two party invitations for Saturday night, don't complicate the situation by accepting a third.
This verb dates back to the 17th century, when it meant “to intertwine” or “to fold together." This intertwining and folding together, however, sometimes don't work out so well. An infection can complicate an injury. A detour for road construction will complicate your usual route. And directions that are written in another language — and without pictures — complicate the assembly of furniture and toys.