In simple language, the more people using something, the more powerful (and beneficial) it becomes.
Think of the very first fax machine. By itself it was useless -- until there was a 2nd fax machine! Suddenly, they could fax each other. As more people got fax machines, the network grew and the usefulness soared. Every fax owner encouraged others to buy fax machines so they could fax more people. Simply using the fax machine was a advertisement for others to buy one. Now, practically everyone has fax capabilities.
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Each new member increases the power of the network which in turn attracts more members. This is a large part of what Malcolm Gladwell talks about in The Tipping Point. After a certain point, network growth is automatic and continuous without further effort.
But this is a complete departure from our human past. The industrial economy was based entirely on the laws of decreasing return. Growth was linear and directly related to effort. Small efforts led to small returns. Economies of scale were mandatory otherwise costs could never be brought low enough for high returns.
The system has been turned on its head however. Networks work exponentially so small efforts (properly applied!) can yield enormous results. Companies that rely on the network experience small early gains until they hit their tipping point, then growth accelerates explosively with minimal additional energy.
Facebook is a great example. With more the 350 million subscribers, how many connections are available to all members? Now imagine the ripple effect on that enormous scale network with 1 new member!
Everything is magnified exponentially because of the network. Respect it and understand how to use it to your advantage.
Learn more about the network effect from Kevin Kelly here.