It's annoying when ads interpose segments of your favorite TV show. When something interposes something else it interrupts it.
If you look closely at the word interpose, you'll see inter- which means "between" and -pose which means "position." Don't think of this only in the physical sense though. It can also mean "interject," or say quickly, and also "get involved in." If you want to interpose when another person interposes himself into a long waiting line, you might interpose, "Hey, you're cutting."
