In a way, all vultures are Time Vultures; some just have more patience than others.
This comic is about the time vulture (hence the title), a fictional creature made up by Randall. Cueball notices that his Cueball-like friend is followed by a time vulture, making the exclamation Dude, you've got a time vulture.
The primary food source for vultures is carrion, or rotting meat. A time vulture, as explained by Cueball, is a type of vulture that can live for millennia (i.e. thousands of years), spending very little energy and it can even slow down its internal clocks so time speeds past, a kind of forward time travel, to the point where its prey dies. In this way, it can thus always wait long enough for the prey to die of natural causes no matter how long it takes, as seen from the prey's point of view. So in principle they kill their prey by using aging, as Cueball explains, although in fact, like any vulture, they just find prey that has already (almost) died, as from their point of view every living thing is just about to die. But as with other vultures, they do not participate in the actual killing. Time vultures thus just need to locate and find any one living creature (of a reasonable size), then it becomes it’s prey as it then just waits until it dies, spending hardly any energy while it waits. Real soaring vultures can also stay afloat for considerable time spans without actually using any energy as they just float on thermals.
Thus the time vulture will now keep soaring over Cueball’s friends head for the rest of his life, and then when he dies (whenever and of whichever cause), it will descend and feast on his carcass. This should, in principle, not make any difference to the friend, since most people already live with the knowledge that they will eventually die, and that their body will end up being destroyed one way or another.
And because the time vulture can slow down its internal clock, in its point of view, everyone who ever says "But, I'm not about to die" (or anything else, really), would say so right before they die. In humans' point of view, it could be many years after the statement was made, but for the time vulture, a human lifespan only lasts a mere moment.
It is thus really more of a philosophical comic about the fact that we all have death waiting for us, you could say it soars above our head and just wait for it to happen. And in relation to the deep time of the geology of the Earth or the expansion of the universe, the time it takes for people to live their lives is hardly worth mentioning...
In the title text it is stated that all real life vultures are actually a kind of time vultures, as real life vultures also sometimes spot a dying animal, not quite dead yet, and then wait for this prey to die. But time vultures are able to wait for many years for their prey to die, whereas regular vultures do not have that kind of time, before they need to feed or land, thus the comment that some vultures have more patience than others.
Real vultures and their preying habits were referenced in 1746: Making Friends, directly in the title text.