To interrupt someone is to interfere in their activity, disrupt their conversation, or to disturb their peace and quiet.
Imagine you're watching reruns of Jeopardy! and your mom interrupts you, threatening to turn off the TV unless you take the trash out. Then your brother interrupts your peace and quiet by shouting answers — wrong answers — at the TV. A special weather bulletin then interrupts your "regularly scheduled program" with a severe thunderstorm warning. And, to complete the job, lightning causes an interrupt (now used as a noun) in the power grid and your electricity goes off.