The D&D Adventurers League is the official organized play program run by Wizards of the Coast for Fifth Edition Dungeons & Dragons.

Typically, AL games are played in game stores or at conventions, but home and online games that follow the AL rules are also legal. The actual logistics of play can vary widely, ranging from a regular home game with a consistent DM to online games with randomly assembled players from around the world or perhaps most commonly to regularly scheduled in-store games with a cast of players and DMs that vary from week to week.

The rules for AL games are described in the current season’s Adventurers League Player’s Guide, the associated Adventurers League Dungeon Master’s Guide, and the FAQ.

A notable difference between AL play and non-AL play is the use of a logsheet. Each adventure that a character participates in has an entry on a tracking sheet that records what adventure it was, who DMed it, how much experience and gold the character acquired, any magic items found, etc.  This allows some rudimentary auditing of a character, although to be clear it is all on the honor system, with no centralized tracking of what adventures any given character has participated in. 

For a more in-depth look at the Adventurers League, visit the sites below.

http://dnd.wizards.com/playevents/organized-play

* Special thanks to Garrett Rooney for posting the excellent description
above on rpg.stackexchange.com.