Other forms: kicked the bucket; kicks the bucket; kicking the bucket
When you kick the bucket, you die. Kick the bucket is an extremely informal way to describe death.
If you're looking for a delicate way to talk about someone dying, kick the bucket isn't the right way to do it — it's a blunt and casual, almost joking way to say "die." The origin is a little blurry, though most experts think it stems from the Old French buquet, a trébuchet or beam from which slaughtered — and possibly still kicking — animals were hung.