Think of a swing.....
Have you ever been on one as a kid? You swing up and down, up and down. Sometimes it can get very high and moves quickly or it can swing low. It changes all the time and unexpectedly.
This is exactly what "mood swings" mean: when a person's mood goes "up and down, up and down" like a swing. It changes rapidly.
A person may wake up feeling very happy but then he/she walks into the kitchen to make their morning coffee only to realize there's no more left! This might alter their mood suddenly and can make them go from being happy to feeling annoyed and angry. "Mood swing" means a rapid change in your state of feeling and emotions, just like a swing! Up and down, up and down.