'Mopery' refers to mopish behavior; that is, acting mopy, dull, dispirited, and dejected.
It may also be used to refer informally and humorously to a violation of a minor or imaginary law or rule. Webster considers this to be slang, but it has its roots in a relatively formal usage. Some jurisdictions have used mopery as an legal term to allow them to arrest unsavory characters; it was closely related to loitering, but was expanded to include things like 'walking down the street with no clear destination or purpose'.
You might also come across an even more informal and joking usage. In the movie Revenge of the Nerds mopery was defined as a very specific inane infraction -- "Mopery is exposing yourself to a blind person." This definition has no basis in anything, but it is very humorous, and therefor quite popular.
References and further reading:
The Word Detective
Some quotes and definitions
What an actual dictionary has to say (not much)