Telling someone romantically involved with you that you are in love with them, completely out of the blue. Making them be completely repelled by you in any romantic way.
A:damn man, i gotta get rid of shelly, Im not into her.
B:just pull a mosby on her, dude.
C:yea man, you can mosby the crap out of her.
Telling someone who you are romantically interested in and who is interested in you as well that you love them, causing them to not feel any romantic interest towards you and freaking them out.
Telling a woman you're interested in and have realized you love at some point you love her, causing her to lose any of the obvious romantic feelings she had for you.
Same for a woman towards a man.
I.e. the exchange between Barney and Robin in How I Met Your Mother, and also the reason for the name itself - Ted Mosby from How I Met Your Mother.
"Tim just pulled a Mosby on Rachel"
"Oh God, he's never going to be able to get with her then. She was talking about how much she liked him just last week too"