Linden Lab is a private company founded in 1999 by Philip Rosedale. Its chief goal is to make a virtual world that is overlayed on top of the world wide web, creating a new place that allows anyone in the world to be whatever they wish to be.
Their current product, Second Life, is their first attempt at this. After spending 4 years in development, it was released "live" in June of 2003. Since then, it has grown phenomenally, attracting almost 100,000 people as of this writeup, and physically simulating over 65,000 square kilometers of space (and growing every week).
Most of the press coverage about Second Life focuses on two things: 1),the fact that 99% of the content in the world are made by residents, not the company (using the tools included in the client to make primitive 3d shapes and combining them for more complex objects, then using a proprietary scripting engine to engineer movements and other behaviors for these objects), and 2), the fact that many folks playing Second Life are making money at it. One resident, who deals primarily in virtual land speculation/development, reportedly makes over six figures in $US per year. Another resident created a tetris/bingo hybrid (called Tringo), and sold the rights to a company that is now publishing it for mobile phones and the Game Boy Advance.
The company's board of directors are mostly entrepreneurs and high-thinking people. The founder, Mr. Rosedale, invented the Freevue streaming video codec, and later worked as a vice president for product development for RealNetworks, before founding Linden Lab.
Since then, the company has attracted brilliant people from such disparate backgrounds as nuclear physics, marketing from Electronic Arts, and the coding genius behind another virtual world, There. The company's culture is extremely open, with many of the employees interacting freely with the residents, something not normally seen with online companies or other MMORPGs.
The company allegedly has yet to see a profit, but is in no danger of folding; they are growing their userbase at around 20% a month, and the investors seem content with keeping that growth rate going.
Future projects by the company generally revolve around Second Life: recently, they have launched their own in-world currency exchange, the Lindex, to provide a safe and easy way to convert their internal currency (the Linden Dollar) into $US dollars. Previously, this was done by third party sites such as IGE.
They continue to improve their main product, with new features coming in roughly every 2 months or so.