Most important thing is elightement mechanic which replaces sanity at the second you step into the island.

Enlightement

Like I said, at the second you step into the island, it'll replace you sanity.

You can imagine it like reverse sanity, you want your sanity high but you'll want your enlightement low.

Before going to island, be sure you have something to decrease sanity (and so enlightement). Because being on island slowly increases your enlightement. Also be sure to enter the island with low sanity so you'll be okay when it replaces.

When you enlightement is high, gestalts will start attacking you. And when it is way too high, even more gestalts will start to spawn around you. Gestalts doesn't deals damage, but they can put you to sleep (Also I'm not sure but if I'm remembering correctly you lose hunger when put to sleep by them).

Note that gestalts are afraid of Shadow magic.If you put a dark sword, night armor or craft a night light on the island, they'll stay away from it.

Altars

Altars are crafting stations for Lunar items. On the island, you can find 3 Altar pieces. Put them together in a Celestial Fissure to access Lunar crafting tab. There's 3 Altars in the game but you'll only need them all when you want to spawn Celestial Champion. Other than that 1 one of them will be enough.

Stone Fruits & Saladmanders

Stone fruits are fruits that growns on the island. You can dig up stone fruit bushes and bring them to your base. You'll need a pickaxe to open the fruits. This fruits are very good for winter. Because different from other plants, they'll keep growing during the winter.

Saladmanders are little animals on the island. They live around little polls on the island. If you throw a bath bomb (You can craft it from lunar tab) in those polls, saladmanders will come near them and then turn to red. They also get some sort of fire attack but I can't exactly remember. If you kill them during this stage, they have a chance to drop dragon fruits.