There are lots of stories in the news today about “Phone-tapping” and “bugging devices”. People who do this are the high-technology counterparts of the centuries-old “Eavesdropper” –someone who listens in to other people’s private conversations.
The eaves of a house are the parts of the roof that stick out over the walls, protecting them from falling water & rain. The space on the ground was originally referred to as the “eavesdrip” and later as the “eavesdrop”. This was the area where people like blackmailers, or even detectives, would hide, hoping to hear what was going on in the house. Such people became know as “eavesdroppers”.