It's not my field, so there actually may be practical applications, but in general mathematicians don't really care directly about applications (unless they do). The result stands on its own merit (and may either help in applications later, or simply as a beautiful result, or may later be useful in the proof of some dependent theorem that does have applications).
But essentially a large part of why this is a big deal is that it was a "long"-unproven conjecture that smart people had looked at over the years and not solved, and expected to take heavier machinery, and that all of a sudden got a really simple proof.
But essentially a large part of why this is a big deal is that it was a "long"-unproven conjecture that smart people had looked at over the years and not solved, and expected to take heavier machinery, and that all of a sudden got a really simple proof.