A lot of mathematical problems that originally seemed important [EDIT:
unimportant], like "how hard is it to factor big prime numbers?" or "what kind of mathematical structure describes composed rotations of a sphere" turned out to be way more important than they seemed. The former is at the root of a substantial amount of cryptography (either directly in e.g. RSA or indirectly in e.g. elliptic curve cryptography) and the latter turns out to form the foundation for quantum mechanics, neither of which was remotely in the mind of people originally considering either problem.
Seemingly simple, but practically intractable, problems like the Collatz conjecture, twin primes, etc. tell us that there's something we don't know about relatively simple structures, and the hope is that by studying those simple structures, we might discover something new that is more generally applicable. The interconnections in math tend to form an extremely dense graph, so these long-unsolved problems tend to have lots of established connections to other questions. For example, the Collatz conjecture would tell us something about computability theory, since the next Busy Beaver number we know little about turns out to depend on Turing machines that encode it (alongside other very similar problems).
Mathematicians focus on esoteric stuff too; it usually doesn't make it into the popular press. "Is the fifth fundamental group of the 19-dimensional Pulasky-Robinson manifold of type III infinite?" is the sort of question that comes up all the time but never makes it onto the front page of HN. Questions like "what's the smallest uncomputable busy beaver number" or "is the twin prime conjecture true" are the ones you'll hear about because they're the ones where the question makes some sense to a layperson.