DNS stands for Domain Name System and it's used for IP to name translations. For example, it's easier to remember google.com, instead of 209.85.135.
104. DNS servers are like huge tables that keep these translations. They work recursively. This means that if a DNS server does not find answers for a certain request they forward it to a superior server, and so on. This storing process can be compared to the process of storing names and phone numbers into your address book. Worldwide, the DNS servers are ordered hierarchically.
Each Internet Service Provider has at least two of them. This enlightens the resolution process. Why there's a need for DNS Servers? - there are billions of IP addresses worldwide, and like stated before, names are easier to remember than numbers - many domain names and IP addresses change daily - new entries (domains and IP's) show up over night due network expansion With that many requests needing handling, the domain name service would be easily overwhelmed if it wouldn't have a caching system, or a well set up procedure of resolving incoming requests. Therefore, the DNS resolving algorithm can be fastened with the help of a caching algorithm. The entries are cached locally and recursively depending on an adjacent value called Time to Live (TTL). This value indicates every DNS Server containing the record that it should keep it the record for TTL time value, until requesting a refresh or an update for the record.
This is why when DNS records get modified there is a certain time until all the recursive DNS servers update their entries as well. Stated the above, it's clear that DNS Services are required for the good use of the Internet.
Andrei Bright is has written articles on DNS Servers, DNS Root Servers, and Find DNS Servers for The Tech FAQ.