From the Wikipedia page 
A cryptogram is a type of puzzle that consists of a short piece of encrypted text. Generally the cipher used to encrypt the text is simple enough that cryptogram can be solved by hand. Frequently used are substitution ciphers where each letter is replaced by a different letter or number. To solve the puzzle, one must recover the original lettering. Though once used in more serious applications, they are now mainly printed for entertainment in newspapers and magazines.
Other types of classical ciphers are sometimes used to create cryptograms. An example is the book cipher where a book or article is used to encrypt a message.
The first use of the cryptogram for entertainment purposes occurred during the Middle Ages by monks who had spare time for intellectual games. A manuscript found at Bamberg states that Irish visitors to the court of Merfyn Frych ap Gwriad (died 844), king of Gwynedd in Wales were given a cryptogram which could only be solved by transposing the letters from Latin into Greek. Around the thirteenth century, the English monk Roger Bacon wrote a book in which he listed seven cipher methods, and stated that "a man is crazy who writes a secret in any other way than one which will conceal it from the vulgar." In the 19th century Edgar Allan Poe helped to popularize cryptograms with many newspaper and magazine articles.
It has been argued that the Voynich Manuscript involves cryptograms: there are various discussions on the web to this effect. However it could be argued that the smooth flow of the script means that the author did not have to think about the nature of the text itself.
The Wikipedia page on the American Cryptogram Association is.