No one wants to spend the whole cruise on the ship, and there are tons of excursions available for those who want to explore the islands.
While it can sometimes be cheaper to book excursions locally, it's worth booking them through your cruise. This will ensure you go with a reputable company, and decreases the risk of you getting ripped off.
If you do choose to book locally, keep in mind that the ship won't wait for you if you're late back. If you're on an excursion organized by your cruise company, they'll be able to get in contact with the ship which will either wait, or arrange for you to get back onboard at the next stop.