Dynamic Host Configuration Protocol (DHCP) is a tool that allows your computer to get its network settings from a central server on your network automatically so you don't have to know the nuts and bolts of setting up networking hardware.
A series of databases that translates web address host names to IP addresses. Servers on the Internet use IP addresses to talk to each other. However, we humans prefer more friendly names. The DNS system consists of DNS servers all over the world that translate our human-friendly web domain name to a computer-friendly IP address.
A DNS Server is a computer that keeps a directory of website domain names and IP addresses. Every computer conected to the Internet has a setting for the DNS server(s) to use to lookup website domain names. Usually this is setup through DHCP.
Each computer on a network is identified by an IP address (or Internet Protocol address). This is a group of 4 numbers ranging between 0 and 255 and seperated by commas. Each web site on the Internet also has an IP address (though one address can be shared by multiple sites).
For example, the IP address of this web site is: 74.208.183.64
A router is a piece of hardware on your network that routes all of the information on your network kind of like the mailroom in an office building. It looks at the traffic going between computers on your network and the outside world and directs traffic between each device.