Linux is part of the Free Software movement founded by Richard Stallman and the Free Software Foundation. Other pieces of Free Software include the Apache web server (which powers more than twice as many servers as the closest competing product), Sendmail (which probably helped deliver every piece of email you have ever received), and the Domain Name Service (which translates human-readable domains like "www.yahoo.com" into numbers that computers can actually use). Free Software is wildly successful on the Internet. You can't always see it, but it is there.
Free Software is good for business. Companies such as Yahoo, Google, IBM and Oracle use Free Software extensively as part of their day-to-day business operations. They use it in their server rooms. They use it on the desktop, too, and not just for the technical staff, but for employees throughout every level of the organization. They do it because it works. They do it because it makes sense. They do it because it solves their problems. Linux is good for their bottom line.
Free Software is about choice. It is about being able to choose who you buy your software and services from. You can get essentially the same Linux operating system from Red Hat, SuSE, or from Debian. You can use whichever professional services firm you like, not just the ones authorized by your vendor. This brings the normal market forces of capitalism to bear and that means lower costs for the user and buyer. File formats are open and well-documented. Anyone can write and sell a word processor which can handle files from OpenOffice, Abiword, or KWord. This means that the user is not locked-in to any one vendor, which makes the vendors more customer-oriented. Choice is good for everyone.
Free Software is about community. It is about being able to talk with your neighbors about your software, and to share freely your problems and resolutions. When you plug into the Free Software community you are immediately given "gifts" of software worth millions of dollars. You don't have to give anything back, but most people want to. Many companies employee people who do nothing but write Free Software and give it away. They do this partly for goodwill, but mainly because they can see the benefits they have received. These benefits far outweigh the costs. Most Free Software is written by volunteers who work in their spare time on projects which are near and dear to their hearts. These people tend to produce very high-quality products because their work is a labor of love and they need the result to be effective. They care. It feels good to work on Free Software.
Free Software is good for society. As the computer industry matures, many hardware devices and software programs become commodities. Linux is the sensible progression in this trend. By enabling widespread deployment of software at low cost, companies, governments and people can do things that were out of their reach just a few years ago.