IP addresses or Internet Protocol addresses are the way in which computers on a network both communicate with each other and know where they all are in relation to one another. An IP address is something like a mailing address for computers on the Internet, which allows your email to arrive at the right place and your Web page customers to see the correct Web site.
Most IPv4 addresses are in the format: xxx.xxx.xxx.xxx
Each set is a number from 0 to 255. So a typical IP address will look something like this: 63.141.53.0
If your computer is on an isolated network (meaning, it's not connected to the Internet), it can be assigned any IP address you would like as long as that number is unique on your network. But as soon as that computer is connected to the Internet it needs to be given a registered IP address (which is generally called an Internet address).
Dynamic IPs - Most ISPs grant what are called dynamic IPs to customers connecting to their network. This means that every time you connect to your ISP you're given a different IP address. It is very difficult if not impossible to host a Web page domain on a dynamic IP connection. As every time you connect your server to the Internet the IP address may change. While it is possible to set up a Web server using a dynamic IP ISP, most service providers frown on this. There is usually a clause stating that you cannot use servers on the account.
Static IPs - When you put up a Web page, the server hosting it has to have what is called a static IP. This is an IP address that doesn't change when you login. Thus, if you're going to host your Web server yourself, you need to get an account with a static IP. Generally these are considered "business" accounts and usually cost slightly more than a dynamic IP account, or they are slower than a similarly priced dynamic IP account.
IP and DNS - The IP address is what your domain name is attached to. While one IP address can host numerous domains using DNS aliasing, each domain needs a specific IP address in order to function. When you buy a domain name, you will be asked for the nameservice that will define the IP. However, if you don't have an IP address attached to a computer, most domain name registrars will host your DNS for you - for a price. You can then redirect that domain to your Web site hosted on an ISP or free hosting server or wherever.