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There are two different meanings of the word cryptosystem. One is used by the cryptographic community, while the other is the meaning understood by the public.
General meaning Edit
In this meaning, the term cryptosystem is used as shorthand for "cryptographic system". A cryptographic system is any computer system that involves cryptography. Such systems include for instance, a system for secure electronic mail which might include methods for digital signatures, cryptographic hash functions, key management techniques, and so on.
Meaning in cryptography community Edit
Typically, a cryptosystem consists of three algorithms: one for key generation, one for encryption, and one for decryption. The term cipher (sometimes cypher) is often used to refer to a pair of algorithms, one for encryption and one for decryption. Therefore, the term "cryptosystem" is most often used when the key generation algorithm is important. For this reason, the term "cryptosystem" is commonly used to refer to public key techniques; however both "cipher" and "cryptosystem" are used for symmetric key techniques as well.