[Schopenhauer asks] in his celebrated essay On the Foundation of Morality, "How is it possible that suffering that is neither my own nor of my concern should immediately affect me as though it were my own, and with such force that it moves me to action?...This is something really mysterious, something for which no basis can be found in practical experience. It is nevertheless of common occurrence, and everyone has had the experience. It is not unknown even to the most hard-hearted and self-interested. Examples appear every day before our eyes of instant responses of this kind, without reflection, one person helping another, coming to his aid, even setting his own life in clear danger for someone whom he has seen for the first time, having nothing more in mind than that the other is in need and in peril of his life..."
(My favorite recent example of this was the Subway Superman Wesley Autrey risking his life to save someone who had a seizure and fell onto the subway tracks.)
Schopenhauer's answer to this question is that this immediate reaction and response represents the breakthrough of a metaphysical realization---namely (as he states the idea in Sanskrit), "tat tvam asi, thou art that."
"This presupposes," he declares, "that I have to some extent identified myself with the other and therewith removed for the moment the barrier between the 'I' and the 'Not-I'. Only then can the other's situation, his want, his need, become mine. I then no longer see him in the way of an empirical perception, as one strange to me, indifferent to me, completely other than myself; but in him I suffer, in spite of the fact that his skin does not enfold my nerves."
"Individuation is but an appearance in a field of space and time, these being the conditioning forms through which my cognitive faculties apprehend their objects. Hence the multiplicity and differences that distinguish individuals are likewise but appearances. They exist, that is to say, only in my mental representation. My own true inner being actually exists in every living creature as truly and immediately as known to my consciousness only in myself. This realization, for which the standard formula is in Sanskrit is tat tvam asi, is the ground of that compassion upon which all true, that is to say unselfish, virtue rests and whose expression is in every good deed."