Computers and other devices have unique identifiers to recognize each other on the global scale. In the Internet IP addresses act as such identifiers.
IP address looks like 126.96.36.199. If the computer's IP address never changes over time it is called a static IP address. If the IP address changes each time the computer connects to the Internet, then such IP address is called dynamic.
Static IP addresses are usually given to servers that perform important functions, such as processing emails, supporting sites, sharing files, etc. There are some Internet Service Providers who give static IP addresses to all their clients by default, but more often it is necessary to make a special contract with the provider to get a static IP address.
Dynamic IP addresses are usually given to users who don't have a permanent dedicated Internet access — those who use modems, DSL or 3G/GPRS for portable devices. In this case, each time the computer connects to the Internet it is given a new IP address from the range owned by the provider.
Thus, computers in the Internet recognize each other by IP addresses. However, human beings find it easier to memorize sites by their names, or domains. It is easier for us to find a search engine by its name, like google.com, rather than by its IP address, like 188.8.131.52.
The DNS service relates domain names to their IP addresses. It can be compared to a phone book in which you find a person's phone number by his name.