Meaning of "Move on"

I've never understood the reasoning for someone to "move on" from a relationship. It's not like you are really going to "move on", you are just trying to tell your heart to stop thinking about that person every second of every minute of everyday until it finally becomes a routine and you don't notice it anymore. That is, until you see that person again, with someone who isn't you, and then you have to remind yourself again.