Short for "make a mission". Used to describe leaving a place to fulfill an action, typically leaving to pickup drinks, food, or going out to accomplish something. More frequently used to describe unplanned outings, but can be used for planned as well.
"Let's make a mish to grab those beers from the 7-11."
"We ran out of pizza so I made a mish to get more."
"No more weed? Time to make a mish."