The monoprint or monotype is often thought of as a halfway stage between painting and printmaking. The process is simple: the artist paints, rubs, or wipes the design directly onto a plate, using a fairly slow drying paint or ink. The fleeting image must be printed before the ink dries. Printing may be by press or by hand, and as the name monoprint implies, one can usually get only one strong impression. The effect must be guessed right from the start; there will be no trial proofs or different states unless the design is redrawn for a second impression. This term is used to refer to any print made in one version and incapable of being repeated. A monoprint cannot be editioned.
Monoprinting does allow the artist unusual freedom and spontaneity.
URL: http://www.originalprint.ie/sh652y.html
[Note: the plate is often fiberglass or a similar flexible, durable and transparent material and you don't carve into the plate. If you do, that allows for repetition of images which is categorized as "monotype." I'm drawn to work that is entirely "unrepeatable" as the above implies.]
More info:
Definition of Monoprint
courtesy of Original Print Gallery in Dublin, Ireland
History of the Monotype by William Jung
For a brief, but to the point history of monoprint and monotype.