Three Military “States”:

AA, which stands for Armed Forces (the) Americas
AE, which stands for Armed Forces Europe
AP, which stands for Armed Forces Pacific

Three “City” equivalents:

APO, which stands for Army Post Office
FPO, which stands for Fleet Post Office
DPO, which stands for Diplomatic Post Office

Based on these constructs, a typical Overseas Military Mail address looks like this:

Name
Postal Service Center + Identifier
APO, AP ZIP

or

Name
Postal Service Center + Identifier
FPO, AP ZIP