"It's worth your while to drive by the Grand Canyon if you're in Arizona." This means that it is worth the time spent to visit the Grand Canyon; it means it is not a waste of time, it is a good thing to spend your time doing.

It is something like 'useful', or 'sensible'. It is used to suggest that doing something would be a good idea, or perhaps profitable. It is usually used to suggest something to someone. It would be worth your while getting a passport before the price goes up. It would be worth your while going home before the storm hits.