Besaid Island is a location in the southernmost section of Spira. It is home to the similarly named Besaid Village which contains Besaid Temple. There are a few other transitory locations as well including the Valley, the Lake and the Port.
Besaid Island and Besaid Village are two of the first sections of the game that you visit at the start of the game. Check out the walkthrough sections below for more details:
4) Besaid Island
The first meeting with Wakka on the beaches of Besaid Island and the journey to Wakka’s village.
5) Besaid Village
Exploring the village and the temple and completing the first Cloister of Trials.
There are no mandatory reasons for revisiting Besaid after you have passed through this area, but if you do return to Besaid Island (or more specifically, Besaid Village) you may run into Dark Valefor. Check out the Dark Aeon section for more information:
You may also wish to revisit though in order to obtain the 
Moon Crest. The Moon Crest is used to create Yuna’s Celestial Weapon called 
Nirvana much later in the game and it can be found in a treasure chest.
