Why do you have to Eavesdrop?

While exploring, you may run across enemies with the option to eavesdrop. It’s important not to startle them until you hear what they have to say. Eavesdropping enemies can give you important information such as unique item locations and tips on how to deal with a boss. To eavesdrop, carefully get close and press the down DPAD button.

You only need to hear their conversation once; if you encounter them again after respawning, you can just kill or ignore them completely. Some good examples of important info revealed through eavesdropping is the location of the Shinobi Axe of the Monkey and the tip to use fire against the Chained Ogre boss.