Your computer accomplishes this by using a Name Server (NS), the NS your computer uses normally defaults to the one supplied by your Internet Service Provider (ISP). However the NS from your ISP may not be the fasted performing or have as many extra features a 3rd party NS providers. The speed with which the NS converts the Domain Name into an IP is the resolving speed. The resolving speed can be affected by various factors such as the speed of the NS server itself, the latency of your connection to the NS and the physical distance of the NS from you. So in order to maximise the speed of your web browsing etc. its important to have the fastest DNS resolving speed possible.
A good and easy to use tool that allows you to test the resolving speed of your current NS, vs various 3rd party ones is Namebench. This tool will send multiple DNS requests from your computer to your current NS and to the 3rd party NS list that Namebench includes by default. It then outputs a report comparing the resolving speed of your current NS vs the 3rd party NS services. It will also recommend the fastest NS for your internet connection. In my case using the DNS Advantage NS gave around an 80% speed boost.
If you’re not so worried about speed, you can also use your NS as an extra layer of security.