biochemistry - Human perception of time depending on age

This is not really a biological answer, but a psychological one:

One important fact to consider is that the perception of time is essentially a recollection of past experience, rather than perception of the present.

Researchers who study autobiographical memory have suggested that part of this effect may be explained by the number of recallable memories during a particular time period. During one's adolescence, one typically has a large number of salient memories, due to the distinctness of events. People often make new friends, move frequently, attend different schools, and have several jobs. As each of these memories is unique, recollection of these (many) memories gives the impression that the time span was large.

In contrast, older adults have fewer unique experiences. They tend to work a single job, and live in a single place, and have set routines which they may follow for years. For this reason, memories are less distinct, and are often blurred together or consolidated. Upon recollection, it seems like time went by quickly because we can't remember what actually happened.

In other words, it can be considered a special case of the availability heuristic: people judge a time span to be longer in which there are more salient/unique events.

Incidentally, (and to at least mention biology), episodic memory has been shown to be neurally distinct from semantic memory in the brain. In particular, a double dissociation has been shown for amnesics who suffer from semantic or episodic memory, but not both.

My apologies for the lack of citations, but a good bit about autobiographical memories can be found in:

Eysenck, M.W., & Keane, M.T. (2010). Cognitive Psychology: A
Student's Handbook.

You may also be interested in some responses or references to a related question on the Cognitive Science StackExchange:

Perception of time as a function of age