Computers handle network traffic much as the post office handles mail. Think, for example, of the steps involved in sending and receiving a letter. Your postal carrier must know where to drop off and where to pick up mail. So your home must have some kind of recognizable interface; we call this a mailbox. And whereas your postal carrier may know your neighborhood quite well, delivery in other areas requires other carriers. Mail is passed to these other carriers through a gateway; we call this the post office. Although you can think of the whole postal system as one big network, it's easier to understand if you think of it as a hierarchy of subnetworks (or subnets): the postal system is divided into states, states are divided into counties and cities with a range of Zip Codes, Zip Codes contain a number of streets, and each street contains a unique set of addresses.
Computer networking mirrors this model. Let's trace an email message from you to a coworker. You compose the message and click Send. Your computer passes the message to a network interface. This interface may be a modem by which you dial up an Internet service provider (ISP), or it may be via an Ethernet connection on a LAN. Either way, on the other side of the interface is a gateway machine. The gateway knows how to look at the address of the recipient of the email message and interpret that message in terms of networks and subnets. Using this information, the gateway passes the message to other gateways until the message reaches the gateway for the destination machine. That gateway in turn delivers the message via a recognizable interface (such as a modem or Ethernet link) to the recipient's inbox.
If you review this analogy, you can easily see which parts of networking you'll need to configure on your Linux system. You'll need to know the address of your machine. Just as the town name Sebastopol and the Zip Code 95472 are two different names for the same location, you may have both a name, called a hostname, and a number, called an IP number or IP address, that serve as the address for your machine.
To translate between these two notations, you may need to know the address of a Domain Name Server (DNS). This is a machine that matches IP addresses with hostnames. You'll also need to know the address of a gateway machine through which network traffic will be routed. Finally, you'll need to be able to bring up a network interface on your system, and you'll need to assign a route from that interface to the gateway.
While all of this can seem complex, it really isn't any more complex than the postal system, and it functions in much the same way. Fortunately, Linux comes with tools to help you automate network configuration.