We often try to deny the basic fact of our own mortality. Death is something that happens to others, old people and sick people, but not to ourselves. But denial is no solution, because in the end death will always get us. And deep down we know anyhow we're all mortal, and then the suppressed fear of death will manifest in all kinds of anxieties.
Rather than denying death, the Buddha urges us to contemplate death deliberately ('Maraṇussati'). Not to resign ourselves to dying, but to follow the Buddha on the Noble Eight Fold Path that will ultimately lead us beyond death. We all can defeat death and realize the same Deathless State of Nibbāna that the Buddha realized meditating under the Bodhi Tree.