Luffy has a grapple ability using his arms which enables him to traverse around the island quickly. To unlock this ablilty you must first play through the tutorial of the game. Once the grapple ability has been unlocked, triangular lock-on markers will appear on man-made surfaces to indicate that it can be used as a grappling point. To use the grappling ability you just need to look at the point and press R1 (RB) to stretch out Luffy's arm and make him grapple over to the point. Luffy's grappling ability can be particularly effective when combined with other exploration abilities such as Gum Gum Rocket.
As well as allowing Luffy to traverse around the island quickly Luffy's grappling ability can also be used as a close-range combo to take down enemies. However before you can do this you will need to unlock the ability by unlocking a couple of skills at the 'Skills' menu. At the very bottom of the 'Exploration' section you need to spend 200 Skill Points to unlock the Lunge skill which will enable Luffy to grapple to enemies and then 300 Skill Points to buy the Lunge + Body Bash skill which will let him hit the enemy with devastating bash when he grapples to them. It is recommended that you invest in these two skills as having this close-range combo will make getting around the combat areas of One Piece: World Seeker easier.
Check out our How to Fly page so you know how to do this as well as how to grapple.