Ancient Greek philosophers -- or at least some of them -- understand their activity as philosophers to be a preparation for death. That is how Socrates describes philosophy in the Phaedo. Because the philosopher is concerned with the soul over the body, and seeks to perfect the soul by its knowledge of the truth about the universe, therefore the philosophical life is a preparation for death at which point the soul is separated from the body.
Regardless of the metaphysical and anthropological differences between the two, Christianity and ancient Greek philosophy are similar in this respect. Paul speaks of baptism, the beginning of the Christian life, as a sort of intentional death undergone through union with Christ's own death (Rom 6). Elsewhere he speaks of putting of the old self, which is effectively dying, and putting on a new self (Eph 4, Col 3). Of course the real perfection of the new self comes at the resurrection, so Christian life is a kind of training for death and resurrection.
Because death is an inevitable reality, it makes sense to prepare for it. To some extent we have to ignore the fact of our death and its unpredictability in order to go on in the world; many people, if they spent much time thinking about their own demise, would be too depressed and anxious to move forward. But for those who want fortitude of spirit, who want to face reality and adjust themselves to it, and especially those for whom (as Athanasius says in De Incarnatione) death is something dead because of the resurrection of Christ, meditation on and preparation for death are essential.
Meditation on and preparation for death are important for at least the following reason: they help us to understand well the finitude and preciousness of time. They help us to use our time wisely; in an interesting way, meditation about the imminence and inevitability of death can inspire a profound, ardent zeal to live and to live well. One of my favorite lines from The Imitation of Christ:
Many have died suddenly and without warning; for the Son of Man will come at an hour when you least expect Him (Lk 12:40). When the hour of death comes, you will begin to think differently about your past life and great will be your sorrow then that you have been so negligent and lazy in God's service.
How happy and wise are those who try now to become what they would want to be at the hour of death (I, 23, 3-4).