If you walk into your kitchen and discover an uninvited neighborhood kid eating your cereal, that kid is a trespasser. A trespasser is someone who enters another person's property without an invitation.
Trespassing is a crime, so a trespasser can find herself in a lot of trouble. As a legal term, trespasser implies that the person has intentionally and knowingly entered private property. So if you trip and fall and find yourself tumbling down a hill into your neighbor's garden, you are not a trespasser. If you stand up, brush yourself off, and enter your neighbor's house to watch their TV, you are a trespasser.