In UK and Australian slang, the word "mong" is used as a vague insult roughly equating to "idiot", "moron", "prat", etc. For example, "Shane you mong, you burnt the sausages". It is generally used lightheartedly, i.e. you can call your mate a "mong" when they do something dopey without jeopardising the friendship.
The origins of the term are heavily debated. The Australian version is almost certainly a shortening of "mongrel", falling under the category of Insults that Question One's Breeding. The British version is either derived from the Australian insult, or is a shortened form of "mongol" (a derogatory term for a sufferer of Down's Syndrome). Naturally the latter derivation is somewhat more offensive and politically incorrect than the former, so the insulter must be careful that the insultee does not perceive it that way.
Mong can also be used as a verb and adjective, as described by Oolong. Although sharing the same derivation as the noun, in this context the verb or adjective is usually equivalent to "stoned". For example, "Let's get monged" (verb) or "He looks very monged" (adjective).