Age is a useful construct for humans. It's an easy to communicate concept based on a shared wall clock we can reference. It abstracts away a lot of more complicated and nuanced factors.

People can accrue all sorts of physical changes at different rates (that still fall within a tight distribution). Some people mentally mature faster than others due to experience, biochemical differences, etc. Some people biologically age faster due to genes, stress, injury, illness, or disease. The volume of UV exposure one receives changes your appearance.

Age happens to closely correlate with so many societal concepts we care about: schooling, maturity and behavioral expectations, dating and marriage, career, having children, getting cancer, dying, etc. Age is universally useful and interesting to us.