Why propagation happens at all
There is no single database of DNS. Instead, resolvers operated by ISPs, public providers, and companies each keep their own cache of answers to avoid asking your authoritative name servers for every request. When you edit a record, your name server updates immediately, but every resolver that already has the old answer keeps serving it until its cached copy expires. That staggered expiry across the world is what people call propagation.
Because caches expire at different moments, propagation is never a clean switch. One visitor in Tokyo may get the new value while another in Berlin still gets the old one. This is normal and temporary, and it is why a change can look 'live' on your machine but broken for a colleague.
TTL is the dial that controls it
Every record carries a Time To Live (TTL), the number of seconds a resolver is allowed to cache it. A 3600-second TTL means a resolver may serve the old answer for up to an hour after you change it. Lowering the TTL a day before a planned change shrinks that window, so the update rolls out in minutes instead of hours.
You can watch propagation happen by querying your domain from many locations at once. This site's checker does exactly that for A, AAAA, CNAME, MX, TXT, and other records, showing which resolvers already return the new value and which are still catching up.