Meaning
Endure pain with fortitude.
Origin
In the days before effective anesthetics soldiers were given bullets to bite on to help them endure pain. Improvements in battlefield medicine has seen the real act of biting bullets migrated into metaphor, although it must still happen occasionally.
First recorded in print in Kipling's Light that Failed, 1891. Kilpling uses 'bite the bullet' rather than 'bite this bullet', which we might have expected if the idea were new to the character being spoken to. That tends to suggest the phrase was already public when the story was written.
...'Going to sleep by you. Lie down now; you'll be better in the morning.'
'I shan't!' The voice rose to a wail. 'My God! I'm blind! I'm blind, and the darkness will never go away.' He made as if to leap from the bed, but Torpenhow's arms were round him, and Torpenhow's chin was on his shoulder, and his breath was squeezed out of him. He could only gasp, 'Blind!' and wriggle feebly.
'Steady, Dickie, steady!' said the deep voice in his ear, and the grip tightened. 'Bite on the bullet, old man, and don't let them think you're afraid,'