A few possibilities come to mind. First and foremost, extra dialog options, both with NPCs and with interactable objects. You see a messy desk covered in books and scrolls. "sage" lets make sense of them (or makes the arcana roll easier). You're about to enter town and the guards seem to want to shake you down. "Noble" allows you to bull your way through, "soldier" allows you to appeal to your shared occupation and get through, "criminal" lets you bargain the bribe down -and- gives you a contact to talk to at the inn about smuggled goods. When Swen showed the scene with the intellect devourer coming out of someone's head, one of the dialog options was tagged "githyanki", so this is not at all difficult to imagine. Option 2: situation specific bonuses to rolls (persuade checks against people of similar background, tasks related to the background). Option 3: they've said insight dice are in the game (and we've seen the option come up as a pop up when Swen failed a roll) - possibly acting in accord with your background is related to how you get them.