Second Life, shortened by most to “SL”, is an online virtual world where anybody with a broadband connection and a reasonably powerful computer can interact, create, educate, play, and work in a graphically-rich 3D environment. It is an immersive space where you interact with your surroundings and other people through an avatar (a representation of a human, or non-human, being) that walks, flies or drives around.
Second Life is a 3-D metaverse (beyond the physical universe) or open-ended platform for communication, socializing, creativity, prototyping, gaming, entertainment, business, non-profit work -- and more.
This software and online interactive environment is not the game you may be used to from The Sims Online or World of Warcraft, although it has some of the same features and you can play various games within it and with it. It is big enough so that you can take it very seriously and make a real income from it, yet small enough so that you can always pull away and say "it's only a game".
Linden Lab is the company that created and maintains Second Life. Lindens are the employees of Second LIfe. "Lindens" is also the name of the game currency.