Yielding is a way of ending a fight started by accident. If your opponent shows a high disposition toward your character, you can ask him to stop fighting by holding the block key and activating the NPC, as if you wanted to talk to him. (In Skyrim, this was changed to just sheathing your weapon and seeing if the person will accept it.)
This works well with human NPCs, but has no chance of working with monsters, animals, or certain quest NPCs. Also, if you commit a crime and choose to resist arrest, you can yield to the guard if you've changed your mind about resisting. This will bring up the same dialogue and menu that appears when you commit the first crime. From there you can pay the fine, go to jail, or continue to resist arrest.
You can use this to your advantage when facing people who like you (such as the quest The Purification). Initiate combat, then yield to your target as many times as you need. However, this may not always work, people with a high aggression stat may still continue to fight, even if they like you.
In The Elder Scrolls V: Skyrim, this was changed to just sheathing your weapon and seeing if the person will accept it.