From Destinypedia, the Destiny wiki
Xbox Live is Microsoft's dedicated online multiplayer subscription service for the Xbox series of consoles, used to play supported games via connectionto the internet. On the Xbox versions of the game, Destiny is expected to use Xbox Live as the service for online gameplay when using the Xbox 360 and Xbox One. Perks of using Xbox Live include access to online modes of Xbox games, voice chat with other players, an in-console LFG service to connect with other players, groups and clans that gather players who play the same games, special discounts on certain games as well as a selection of free games that rotate once a month, and many more. Players can subscribe to Xbox Live in either 1 month, 3 month, 6 month or 1 year subscription passes that can be bought in the form of a code either in-store or online.
GamerTags are used to keep track of the players recently played games, Gamerscore, and Reputation rankings, among other things.