The meaning of intruder / intruding in dream | Dream Interpretation
Dreams of an intruder represent that you are processing and venting your fears of being hurt or having your boundaries violated.
The intruder can also represent your unintegrated shadow that will continue to threaten you until you face and embrace it.
If you dream of being the intruder, then your dream is giving you the message to only go where you are invited, and not to waist your time and energy attempting to put your energy where it is not desired or appreciated. See Integration Dreams and Burglar.