D&D can be described as following:
The core of D&D is storytelling. You and your friends tell a story together, guiding your heroes through quests for treasure, battles with deadly foes, daring rescues, courtly intrigue, and much more.
Starting D&D with brand new players can be very challenging and very rewarding. There are many guides to get started, but the best way is just to dive in. Gather a few players together, designate someone to run the game (as the Dungeon Master), make some characters and play.
For players who wish to get started with the latest edition, the rules are available for free download.
Several older editions, such as 1st Edition and 3rd edition, have open source re-implementations available for download.
The equivalent of 1st Edition D&D is OSRIC, the Old School Reference & Index Collection.
The equivalent of 3rd Edition D&D is SRD, the d20 System Reference Document.
Some introductory videos to get oriented to D&D: