As I said some 6 weeks ago, in my first blog on Heidegger, the basic idea in Being and Time is very simple: being is time and time is finite. For human beings, time comes to an end with our death. Therefore, if we want to understand what it means to be an authentic human being, then it is essential that we constantly project our lives onto the horizon of our death. This is what Heidegger famously calls "being-towards-death". If our being is finite, then an authentic human life can only be found by confronting finitude and trying to make a meaning out of the fact of our death. Heidegger subscribes to the ancient maxim that "to philosophise is to learn how to die". Mortality is that in relation to which we shape and fashion our selfhood.
There are four rather formal criteria in Heidegger's conception of being-towards-death: it is non-relational, certain, indefinite and not to be outstripped. Firstly, death is non-relational in the sense in standing before death one has cut off all relations to others. Death cannot be experienced through the deaths of others, but only through my relation to my death. I will contest this criterion below.