An IP address is a unique address used to locate and identify a device over a network. That device can be an electronic device, a computer, a server, a router or even an IP phone. It is the addressing used for the transmission of data packets over a network working with the IP protocol.
 The IP Address Structure
All IP addresses are made up of four parts (quadrants) separated by dots, like this:
where each XXX can be any number between 0 and 255. If you know binary, you will understand that each of these numbers are stored in 8 bits (binary digits), and the number of possibilities you can have is 2 raised to the power of 8, which is 256 (0-255).
Examples of IP addresses are:
The second example above is the default IP address assign to any standalone machine. So, if your machine is not connected to any network, its address is 127.0.0.1. This is also called the localhost address.
 The two parts of an IP address
An IP address consists of two parts: the network part and the machine part. Let us make an analogy to your house's address. It is made up of the country part, then the city part, then the street part. All people living in your locality will have the same country and city parts in their addresses. Only the house number and street parts will be different.
For IP, all machines on a same network will have the same left (network) part. The right side varies based on machines. For example, right now, I am writing this within a LAN. The LAN router's IP address is 10.15.30.1; my machine's IP address is 10.15.30.5 and my fellow LAN-mate's IP address is 10.15.30.6. In this LAN, the network part is 10.15.30 and the machine part is the last quadrant. We can have a maximum of 256 machines on our LAN. Bigger networks have smaller network parts and bigger machine part, so as to accomodate more machines on the network.
 Dwindling IP addresses
An IP address carries 32 bits (8 for each quadrant). This can give up to around 4.3 billion addresses. Unfortunately, many of these are wasted. During the early days of the Internet, big companies bought large chunks of IP addresses and till now can never use all of them. The current version of IP addresses in use is version 4, called IPv4. Since it is predicted that the time where IP addresses will start lacking on the Internet, a new version has been developed. IPv5 has been only for research purposes. The next version is version 6, IPv6. This takes 128 bits to store an IP address, so you are sure to get enough addresses for the next centuries! IPv6 will take some time to come. The transition fromo IPv4 to it is a challenge.
 How are IP addresses assigned
So as not to have any duplication or inconsistent in the allocation of IP addresses, there is an independent organisation (like there are so many working on Internet technologies) that takes into charge the allocation of IP addresses. It is called the ICANN (International Company for the Assignment of Names and Numbers). Before the creation of the ICANN in the 90's, there was the InterNIC doing that work.
 Names to IP addresses
If you have a web-site, it has to have a domain name, which, simply said, is the what you type to access its main page, e.g. about.com, google.com. Just like IP addresses, each of these domain names have to be unique. You cannot have two sites with the same name and address. Each name is attached to an IP address. The ICANN takes care to ensure that all names and IP addresses are unique.
When a user types the address of a site on a browser, the name is converted, or rather matched, to its IP address at a DNS (Domain Name Server), which is there for domain name translation to IP address.
 Buying IP addresses
If you want to get one or a set of IP addresses, you have to buy these from IANA (Internet Assigned Numbers Authority). But you do not necessarily need to do so directly. Say you want to create a web site and name it [ somethingelse.com ] you can go to any of the domain hosting companies - where they ask you to choose a name (and they check whether [ somethingelse.com ] is unique) and you pay for their domain hosting services. They also assign an IP address to your site. They check all this with IANA.
 Dynamic Allocation of IP Addresses
Your computer, router and IP phone do have IP addresses, which you never set. These addresses come automatically and they are not permanent. They change each time you start a new session.
Your ISP (Internet Service Provider) has a pool of IP addresses which it distributes to a user once they connect. These addressed are recycled and redistributed to other users once they are free. This is carried out automatically using a protocol called DHCP (Dynamic Host Configuration Protocol).