I recently learnt this expression from a friends of mine. You use it when someone's irritating you and you tried as much to shoo him away, only to end up getting worked up for nothing. Biar. Eventually he'll get the hint. No point getting mad about it.
Or when someone's being kiasu and wants to know every single thing that you're doing at work (to stay competitive, or at least not behind me) and basically 'parrot' whatever you say or do. Eventually that person for sure could not put up the act that long.....
Or when you feel like you're exploited, and no matter how many times you've voiced it out, nobody gave a damn anyway. BIAR! you'll have the last laugh when you tender your resignation!