A TTL of 300 means five minutes. 3600 is an hour. 86400 is a day. Lower TTL means faster change visibility and more query traffic. Higher TTL means snappier repeats and slower cutovers. Authoritative servers can also send a negative TTL (from SOA minimum) that controls how long “this name does not exist” is remembered — which is why a typo can seem to linger after you create the record.
Planning a move
You cannot lower TTL retroactively for people who already cached the old value. Drop TTL to 300 at least one full old-TTL window before the change. After cutover, confirm with DNSFetch, then raise TTL so you are not DDoSing your own nameservers.
Some anycast CDNs ignore your origin TTL and cache at the edge on their own schedule. In that case “I set TTL to 60” does not mean users see changes in 60 seconds.
See also propagation and caching.