A network effect is a business model that becomes more valuable the more people use the product or service the business provides.
Network effects are oftentimes the result of a first-mover advantage and usually quite durable. They're reached when each additional node added to a network enhances the value of all the existing nodes. For example, each new seller that joins the eBay auction site adds to the breadth of products, thus enhancing the buyers' experience and likely begetting even more buyers. And in a virtuous circle, more buyers begets more new sellers.
The greater the size of the size of the network in relation to the market, the stronger the power of the network. Some networks are so powerful that electing not to opt into the network is disadvantageous. For example, a retailer who chooses not to accept Visa cards puts himself at a significant disadvantage to his rivals, presumably all of whom are part of the Visa network.