Something that is trespassing is slowly intruding into where it doesn't belong. A trespassing stranger is breaking the law.
If you've ever seen a "No trespassing" sign, you probably know it means "Keep out!" Similarly, anything described as trespassing is creeping or otherwise moving where it doesn't belong. Trespassing kids are playing in the neighbor's lawn. A trespassing dog is getting into the chicken coop. A trespassing tree might be growing where it shouldn't be and needs to be trimmed. This word always describes people, animals, and things that go where they shouldn't. Trespassing things are invasive and encroaching.