When changing DNS settings, I'll sometimes see a TTL ("time to live") field. When I'm adding new records or changing settings, I'm usually warned that "full propagation can take 2-3 days," so I always set the TTL to the lowest possible time.

Why choose 1 day when I can choose 2 minutes?

What's happening "under the hood" and when should I choose a short TTL versus a long TTL?

Please, explain it like I'm five!