It depends on your aging setting. On short, it really happens every day. On long, it doesn't happen too often. On normal, so so.
The calendar birthday shows on what day sim has 24 hours or less left so you can plan a birthday party. Sims usually age up the day after that.
If you're planning to do rotational play and don't want other households to age up while you're not playing with them, go to gameplay options and set the aging so that only the active household ages. By that way, unactive household's sims' birthdays get pushed forward on the calendar until you play with them again. And never accept invitations if somebody invites your sim to their birthday party.