Here are some examples:
* "I'm sorry to intrude, but I need to speak to you for a moment." (interrupting someone)
* "The paparazzi intruded on the celebrity's privacy." (entering a place without permission)
* "The noise from the construction site intruded on our peaceful afternoon." (interfering with something)
Intrude implies an unwelcome or disruptive action. It suggests that the person or thing intruding is not wanted or is interfering with something else.