Cryptology is the study of cryptography, the construction of codes and ciphers, and cryptanalysis, the study of analyzing and breaking codes and ciphers.
But it is also much more. Cryptographers study any sort of interaction or protocol that needs to be carried out correctly in the face of adversaries (real or imagined). This can mean sending secret messages over an insecure network, creating fault tolerant computer systems, or verifying the identity of someone you have never met.
As an example of the broad scope of cryptology, consider the following problem: You and I both know some secret and want to verify that we know the same secret without revealing any information about the secret itself. We want to, for example, prove to each other that we're both in possession of Colonel Sanders secret recipe without giving it away. I could pick a number n at random, ask you the nth ingredient, and then verify that your response is in fact correct. Then you could do the same for me. However this is a terrible way to go about it because if I don't really have the secret recipe then I can steal it from you by just pretending that I do and asking you questions.
So how can this be done in a way such that it is provable (in a mathematical sense) that no information about the secret "leaks"? Cryptographers have come up with the answer: zero knowledge proofs.
Cryptology draws on many related fields including probability, computational complexity, theoretical computer science, coding theory, number theory, the theory of computation, and information theory.
Typical problems tackled by cryptographers are the creation of secure encryption schemes (both public key cryptography and private key cryptography), authentication, zero knowledge, PCP (Probabilistically Checkable Proofs), fair auctions, digital cash, anonymous cash, oblivious transfer, and data integrity.
As a final note on surprising results obtained in this field, consider that cryptographers have come up with a way that people can play poker without any cards and with full confidence that no one can cheat. It's called mental poker.