In this poem, the author expresses the idea that death is not an isolated event. that a death affects everyone, or should affect everyone:
Each man's death diminishes me,
For I am involved in mankind.
It sees mankind as being part of a greater creation so that the death of an individual does not occur without some resulting action. The metaphor used is comparing each man to a part of a continent and with an individual death, a piece of the continent falls away:
Each is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less
Donne was a metaphysical poet and often wrote about themes of death, religion, etc. This poem expresses the Biblical idea that man is part of the body of Christ and has importance both as an individual and as part of that greater body. The body cannot function as well when it is missing a crucial part, so that the loss of any part of the body affects the entire body. As in this poem, the loss of any one man affects the universe.
So, when you hear that bell toll, don't ask yourself, "Gee, I wonder who died," because the bell is tolling for you! Maybe you are not the one dying right now, but you will be one day, and the one dying right now is a loss for everyone.