to abandon, to give up, to renounce, to cease trying to continue, to desert, to leave, to withdraw from.
To abandon a plan, idea or an initial intention of doing something.
To leave or dump a girlfriend/boyfriend.
Oh this restaurant is full... shall we bin off this one?
Yeah let's bin it off and go to Burger King.
I wanted to go to Ibiza this summer but it was so expensive so I decided to bin off that idea to go to Benedorm instead.