(in psychology) "the attribution of one's own ideas, feelings or attitudes to other people or to objects; esp: the externalization of blame, guilt, or responsibility as a defense against anxiety"1

— or — to paraphrase Dorland's Medical Dictionary: a mental defensive mechanism whereby a "repressed complex" is concealed by being assigned as the property of the world at large or as a property of someone besides the person who is engaging in the projection.

Psychoanalytic terms, including "projection" and "transference," as they apply to a therapeutic setting (and most specifically, a setting in which the analysand is a child) are discussed in brief at:

http://www.psychematters.com/papers/mawson.htm

The page referenced discusses these terms in the context of "psychoanalytic play technique as devised by Melanie Klein." The author is psychoanalyst Chris Mawson.

Another interesting source for definitions on these matters would appear at the C.G. Jung Page. "Projection" is defined at:

http://www.cgjungpage.org/jplexiconi2p.html

and includes the comment that "transference" and "countertransference" are each terms used specifically to identify the type of projection that occurs commonly in a analyst-analysand relationship, refering respectively to projections by the analysand and by the analyst.

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1 Webster's Ninth Collegiate Dictionary