Someone who cleans people and or situations up. Like how a mop cleans the floor, a moppy person makes those around them better. Typically an attribute of people named Taylor. Also if a person is moppy its a safe bet they are also pretty.
I used to carry around money in a sock and be belligerently drunk a lot of the time until my moppy girlfriend used her moppiness powers on me. Now I only do those things occasionally.