Like G.I.Bro said, the androgenic component of AAS are the main culprit, although they don't actually "age" us any faster...at least not significantly.
Rather, we become more heavily androgenized, which can be misinterpreted for aging. Through prolonged steroid use, we more quickly max out the body's capacity for change in this area, but once its done, it doesn't go any further.
On the other end of the spectrum, androgens can also have the opposite effect on appearance as we get into our older years. Have you ever seen a 70 year old steroid? I have more than once and in all cases, they appear to be much younger than your typical skinny-fat, frail, sickly, beaten down by life looking 70 year old. Older steroid users have defied time. They look strong and capable. Their movements are unimpeded and fluid. They walk with the confidence and air of a man 30 years their junior. They are more exuberant and exhibit a zest for life. Their overall disposition exudes virility and vitaity. They look like they could and still do bang women .
Of course, steroids don't guarantee any of this stuff, but the potential is there. They can turn back the hands of time by preventing osteporosis and maintaining or increasing muscle mass beyond what the individual displayed decades earlier. They jack up libidio and improve overall sexual, physical, and mental functioning. Basically, they allow you to maintain the qualities associated with youth.