To "interrupt" someone is to make them stop doing what they are doing. You can interrupt people while they are:
- talking to someone (interrupt someone's conversation)
- thinking about something (interrupt someone's train of thought)
- writing something (interrupt someone while they're writing)
- watching TV (interrupt someone's show)
You usually follow the word "interrupt" by telling who you're interrupting:
Sorry for interrupting you.
But you can also leave it on its own:
I hate to interrupt, but can I speak to you privately for a minute?