In both the book and movie 2001, astronaut and scientist David Bowman is on a mission to track the source of an alien artifact found on the moon, which leads to a moon around the planet Jupiter (in the novel, Saturn); the story takes place in the year 2001.
The visual representation of David Bowman's new state in the movie(s) is that of a variety of human David Bowman bodies at various ages (from embryo to elderly).
The second name "Bowman" is assumed to be a reference to Ulysses, whose skill with the bow is often described in the Odyssey.
Faced with the prospect of disconnection, HAL proceeds to kill Poole while Poole is repairing the ship, as well as the other members of the crew who are in suspended animation by disabling life support systems for the suspended animation chambers the crew is placed in.
Bowman shuts down HAL by removing modules from service one by one; as he does so, we witness HAL's consciousness degrading.
HAL was also "featured" in a short commercial by Apple Computer in the year 1999 in which he asks Dave if he likes his Mac more than him (because Macs would not undergo the same potential problems with the "Year 2000 problem" that many other computer systems were expected to have).