Martin Heidegger, a German Philosopher, makes the claim that human existence is temporally ecstatic (ecstatic being derived from a Greek term meaning "standing out"). Humans live as always outside of ourselves in time, projected toward the future so that we're always, in a sense, ahead of ourselves through the plans we make and, at the same time, thrown into our present from a particular past. More important for our purpose, the temporally ecstatic way in which humans exist means for Heidegger that we fundamentally are our own possibilities. The possibilities we've chosen in the past determine the concrete possibilities that are available to use in the present and the way they appear to us, while our being projected into the future determines how we'll relate to those present possibilities.
Ultimately, Heidegger's point is that what and where a person is at any given instant is far less important to understanding human existence than that persons past and their plans for the future.
For Heidegger, human existence fundamentally consists of it's own possibilities, and of course, death would be the limit of those possibilities. But for Heidegger, the significance of death is not that it is a literal end to ones life, like a sort of end point on a line, but rather it makes human beings aware of the fact that their own lives, their own possibilities, have a limit. That is, although we exist in a temporally ecstatic way, we are also temporally finite (limited), and what's more we know it. As Heidegger would say, "Initially and for the most part," Humans don't think about their own deaths; we find ways to cover over death and avoid it. We busy ourselves with our projects, with our entanglements in the things at hand, and generally think of death as something that happens to other people. Admitting to ourselves that "people die" is easy enough, but there's something unnerving about thinking "I will die." Heidegger terms that uncomfortable feeling of authentically confronting the certain possibility of one's own death.
Heidegger argues that death appears as what it really is: the possibility of my own impossibility. Once I die, I will no longer have my possibilities. After death, all my choices will have been made already, and the story of who I am will be complete. This is why Heidegger claims that the authentic confrontation with death individuates human existence. When I confront my own death, I see that it is something that no one else can do for me, something I will have to face myself. This in turn casts my whole life in a new light. Recognizing my death as the unavoidable end to my own life shows me that existence is mine and mine alone. The complete story of my life will be the results of the possibilities I chose for myself from out of the situation into which I was thrown at birth. I alone will have been responsible of whoever I was.
(Introducing Philosophy Through Pop Culture Pg.217-218)