Cryptanalysis is the subfield of cryptology concerned with how to "break" cryptosystems. Usually this means breaking a code or cipher in such a way that you can decrypt arbitrary messages that you intercept.

Cryptanalysis is in essence the study of extracting information about something unknown. In the traditional sense, this means extracting the message from the ciphertext without knowing the key. However the term cryptanalysis applies equally well to deciphering an ancient codex written in a long-dead language.

The important part about cryptanalysis is the analysis. A cryptanalyst deems it a success if they can extract even partial inforation from a ciphertext. For example, knowing when the same encrypted message is sent twice can be helpful. If your enemy mounted a major attack after receiving the message 1 20 20 1 3 11, you definitely want to know when that same message is transmitted again!

The fact is, modern cryptanalysis almost never fully breaks a cipher! Cryptographers these days are that good.

David Kahn's masterpiece The Codebreakers is universally acknowledged as the definitive history of cryptanalysis. It is a fascinating read and covers topics such as the Navajo code talkers of World War 2.