Eavesdropping allows you to know what kind of dormmates your opponent has and the odds of you winning a attack against them. Using these details could potentially help you get an additional edge against your opponent. If your question is just "what does the percentage tell you?" The % you see is just the chance you can land successfully on the player. So if it said "5-15% chance of winning an attack", that means you have have 5-15% probability to win a attack.
Further general game questions can be asked on the designated thread here. Or you can join the pimd discord server and ask in the advice channel.