So the modern Internet uses IP packets to communicate, and most of these IP packets use TCP inside. Special nodes called `routers' connect all the little networks together into larger networks, and pass these packets through to their destination. Most normal machines are only attached to one network (ie. have only one interface), and so are not routers.
Every interface has a unique IP address, which look like `22.214.171.124': interfaces in the same network will have related IP addresses, with the same start, the same way that phone connections in the same area have the same prefix. These network addresses look like IP addresses, with a `/' to say how much of them is the prefix, eg `126.96.36.199/16' means the first two digits is the network address: each digit represents 8 bits.
Machines are given names by the Domain Name Service: programs ask name servers to give them the IP address, given a name like `www.linuxcare.com'. This IP address is then used as the destination IP address to talk to that node.
Rusty is really bad at writing documentation, especially for beginners.