Gili Trawangan is a part of the Gili Islands (Gili Air and Gili Meno being the other two), and is situated in Bali, just northwest of Lombok. Trawangan is the biggest of the three. Gili Trawangan hostels are a popular tourist and backpacker destination, mostly because of the island's nice beaches, diving, snorkeling, and parties, but also for other activities. Trawangan is reachable from the mainland by ferry or boat, with multiple options available (combination bus+ferry tickets etc.), see the local transport operators for details.
An interesting piece of information about the Gili Islands is that there are no motor vehicles allowed on any of them. None. This means that your main form of transport around the islands (if not using your feet or a bike, because the islands are small and easy to walk around) are horse-drawn carts, which is actually an exceptionally nice way to travel in the area and also a sound environmental choice. Something else to note is that, of the three islands, only Gili Trawangan has an ATM. Also, there are small medical care facilities on all of the islands, but should any major injury occur, you will need to be transported to Lombok or mainland Bali.
Like mentioned before, the main things to do when you're visiting Gili Trawangan hostels involve the sea. In addition to snorkeling, diving, and general beach life, surfing has also been possible in the islands for quite a while. Please bear in mind that the locals are Muslim, so sunbathing without clothes or wearing provocatively little clothing outside of the beach is not considered respectful, and you should avoid it. That being said, the people of the Gili Islands are extremely friendly and open-minded.