It's annoying when advertisers interpose commercials between segments of your favorite TV show. To interpose is to interrupt by placing something in between other things.
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 between you and your friend in a long queue, you might interpose, "Hey, no cutting!"