To "blow someone off" means to ignore them, not listen to what they're saying, and to do things to quickly get rid of them.
Imagine that there's a piece of hair on your finger. To get rid of it, you blow it off. "Blowing off" a person means to treat them kind of like that piece of hair.
"Blowing (someone) off" has a negative association. It's a pretty rude way to treat someone.
You can also blow off an event, like a party. To "blow off" an event means to just not go to it, in the same light way:
I didn't feel like going, so I just blew it off.
Blowing off an event is not as rude as blowing off a person.