It means that the older someone gets, the more life experience they have, so the more they know and understand. Unfortunately they have the most experience just before they die. So it was the passage of time that gave the experience, and the same passage of time killed them.

It's a joke, a rather bitter joke. "Time is a great teacher" is a saying or proverb. It suggests that the best way to learn things is slowly and naturally, through life experience over time. Your sentence makes a joke by taking that saying and adding an ironic twist to it. It means that life is short, so we don't have the luxury of learning things slowly.