TTL, time to live, is the number of seconds other servers may keep a cached copy of a DNS record before they must check it again. A record with a TTL of 3600 can be remembered for up to an hour. It decides how quickly a DNS change is seen everywhere.
How it is used
Every DNS record has a TTL. Long TTLs mean fewer lookups and slightly faster visits; short TTLs mean changes take effect sooner. Many providers default to somewhere between five minutes and a day.
The common trick before a planned change, such as moving a website, is to lower the TTL on the records that will change a day or so in advance. When the change is made, caches expire quickly and visitors reach the new server within minutes rather than hours. Once everything is settled, the TTL can go back up.
Why it matters to a business
"DNS propagation" is mostly TTL at work: servers holding on to the old answer until their cached copy expires. Planning for it is the difference between a switchover that takes minutes and a day of some customers seeing the old site and some the new one.
Some changes cannot be sped up this way. When a domain's nameservers change, the cache time is set by the registry, not by you. What happens when you change your domain's nameservers? explains why.