To fully commit to completing a task, at the expense of your dignity should you fail/not attempt to do so.
Guy 1: 'why are you downing all your drinks?'
Guy 2: 'I have to; Backed myself!'
'I'm not gunna sleep tonight, gunna last until sunlight.....Back myself!'
Guy 1: 'Im gunna smash her tonight!'
Guy 2: 'Back yourself.'
Guy 1: 'Backed!'