Exercise 3: What TTL Is, and Why DNS Changes Take Time to Propagate — Possible Solution
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What TTL is:

TTL (time to live) is a value set on a DNS record that tells every
DNS resolver that looks up that record how LONG it's allowed to cache
the answer before it has to check back with the authoritative DNS
server again for a fresh copy.

Why a change might not be visible to everyone immediately:

DNS answers aren't looked up fresh from the authoritative server every
single time -- resolvers around the internet (a user's ISP, their
operating system, their browser) cache the answer locally for
efficiency, for however long the record's TTL says they're allowed to.
If a record has, for example, a one-hour TTL, then any resolver that
happened to look up and cache that record shortly before the change
was made won't ask again -- and will keep serving the OLD, cached
answer -- until that full hour since ITS OWN cache entry was created
has elapsed.

Because different resolvers around the world cache the record at
different times, they don't all expire their cached copies
simultaneously -- some may have cached it minutes ago (and will keep
serving the old answer for nearly the full TTL period still), while
others may have cached it much earlier and will refresh sooner. This
is why a DNS change can appear to "work" for some users and not others
during the propagation window, purely as a predictable consequence of
each resolver's own independent caching timeline, not because
anything is actually broken.

WHY THIS WORKS AS AN ANSWER
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This explains the mechanism the chapter names directly ("a value on
each DNS record controlling how long resolvers around the internet
are allowed to cache it") and extends it to explain the specific,
common support observation of INCONSISTENT propagation across
different users -- which follows directly from each resolver caching
independently on its own schedule, rather than everyone refreshing at
the exact same moment.