What does each of the address types indicate?

See definitions:

Primary – Mail will be sent to the address in the primary fields.

Secondary – Like special mail – mail is sent to an alternative address instead of the primary address such as a PO Box.

Sponsor – Use when the parent/guardian lives at another address than that of the patron.

Care Of – Use when the parent/guardian lives at the same address. Place the name of the parent/guardian in the address field.

None – They will not receive mail.