Funny story ahead!
It's called "eavesdropping." This is because of the first person to eavesdrop. The word wasn't invented back then, of course. This first person was a boy, not quite a teenager, who had older siblings. His big sister went on dates a lot, and at his age the boy was really curious about what dates were. Finally, one night, his sister and her date were standing on the front porch. The boy had happened to see them come home, so he very quietly climbed out of his window on the second story and crawled to the edge of the roof to listen in. He couldn't hear anything, so he risked peeking his head over the edge.
He got a glimpse through the eaves of the couple kissing passionately. The boy was so shocked that he lost his grip on the roof and dropped, crashing to the ground. His sister marched over to him angrily and demanded to know what he was doing up there. He had to come up with an excuse fast, so he said, "Oh, just eavesdropping."
And so we have the word today.
(No, this isn't a true story. It's just a punny one.)