Cryptosystem
A cryptosystem is a means by which one can transform 'clear' (i.e. original) data to 'encrypted' (i.e. hidden from view) data - i.e. it rearranges it in a way which is not easily reversible, by an arbitrary outsider. A cryptosystem consists of an algorithm, used to effect the transformation (everyone using a particular cryptosystem has to know the algorithm; in fact, they are now usually widely publicized, although historically they were not) and a key (known only to the entities which are privy to a particular communication, one 'secured' with that cryptosystem and key).
Starting with the 'clear text', the application of the algorithm, along with the key, produces 'encrypted text' (from the original clear text).
A cryptosystem can be used to hide information from third parties (if one sends only the encrypted form of the information to someone else, a third party somehow obtaining a copy of the encrypted text cannot make any use of it), or secure (also called signing) information (i.e. guarantee that a block of information is exactly that produced by the original sender).
To do the latter, the originator produces a checksum of the original data block, and encrypts that with their chosen cryptosystem and key. Even if the original data block is then made widely, publicly, available, anyone who shares the key can verify that the copy they have received has not been tampered with, if they have a copy of the originator's computed checksum; they recompute the checksum, re-encrypt it, and see if it matches that provided by the originator.
