An aging program was a program which could be incorporated into synthetic forms of life, both androids and holograms, to simulate the appearance of aging.
Data had an aging program designed to simulate the external effects of aging in his physical appearance. (TNG: "Inheritance")
The Doctor added an aging program to his matrix around the 27th century to put organics at ease. He preferred to describe his mature appearance as "distinguished, professorial, ruggedly sophisticated." (SA: "Kids These Days")
The aging program is a writing conceit to allow the same actors to portray non-human characters who conceivably should not otherwise age.