All internet client software relies on a resolver. Do you use a web broswer? You need a resolver. Want to upload a file via FTP? You need a resolver. Want to do IRC? You need a resolver. Resolvers allow you to find the IP of the host you are communicating with. Need to know what that IP address is and who it belongs to? You need a resolver and whois.
The resolver is a piece of software that attempts to take the name of an internet host and turn it into an IP address or reverse resolve the IP address back to a host name. A resolver does this by sending a request to a Domain Name Service Server. This request asks the local DNS server to perform a recursive lookup of the host name in question. By making the request a recursive request, the client is asking the local DNS server to ask other DNS servers for an answer if it does not contain the answer itself.
Some systems perform this recursive lookup themselves, but this is becoming more rare today. The Domain Name System makes provisions for client software to perform their own recursive lookup by providing a field in the DNS query packet where the values representing recursion requested and no recursion requested may be stored. Thus, the DNS server receiving the query knows by the query whether it should look up something itself or just point the client in the right direction. By default, most client resolvers use recursion requested.
Resolvers usually are paired with a memory called a cache. Note that if the host receives a negative answer (host/domain not found) that negative answer will be stored in the cache.