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?