Well, 'al dia' can be used in different cases, for example, 'al dia' means 'per day'.. But it can also be used in a sentence like this one: 'I need to get myself updated' which would be 'necesito ponerme al dia'. In that case 'al dia' means 'on time', meaning that you catched up and there's nothing else to do.. Hope it helped :)

Cuando tu dices que tienes que ponerte "al día" con las cuentas, it does mean, que tu tienes que pagar todos los servicios públicos. Ponerte "al día" con las tareas de la casa, el colegio, la universidad, o las tareas de tu oficina.

"Al" is the contraction of "a el". It's the masculine form of "a la". "Al dia" usually means "per day". "A la semana" is "per week".