Tragedy has certain defining conventions: the hero usually has a tragic flaw, the play generally has a mood of foreboding, the hero experiences bad luck/fate (in contrast to a comedy, where at least one lucky break often rights events), and people (usually) die at the end.
King Lear has these salient features in abundance. Lear's tragic flaw is that he suffers from poor judgment, both in deciding to give his kingdom lock, stock and barrel to his two evil daughters, in banishing Kent, and in disowning Cordelia in a fit of a rage because she flatters him insufficiently.
The play grows dark almost immediately. It is almost astonishing how quickly Lear's daughters turn on him: by the end of Act I, Lear has already been cruelly driven out of Goneril's home through her deliberate machinations and both daughters are conspiring to control and humiliate him.
One piece of bad luck which comes at the end is Cordelia's death. Edmund, who is dying, wants to redeem himself and save Cordelia from execution, but he is too late. This tragic event overwhelms Lear.
Dead bodies abound by the end of this play: Regan, Edmund and Cordelia are killed, Goneril commits suicide, Gloucester dies, and Lear is so overwhelmed that he dies of grief.