A polysynthetic language is one which admits the formation of arbitrarily long words of up to a full sentence in meaning; supposedly, for instance, there is an Inuit word which means (and here I paraphrase, from memory): »Here is a little box which I have made for you out of tin so that you can keep fishhooks in it«.
The great majority of polysynthetic languages belong to the three American language groups — the Eskimo, Amerind and Na-Dene groups — although there are exceptions, such as Ainu, the language of the eponymous Japanese ethnic group, and various tiny languages of Siberia. The strangeness of this property has led various people to postulate a genetic relationship between all these languages, a migratory path sweeping from modern Russia, over the Bering Strait, through the American continent and onward into the Pacific — but this is almost certainly hogwash, because the fact is that many other languages exhibit similar traits; notably, many Germanic languages, including German, permit large agglutinations in nouns. Consequently it is more probable that polysynthesis is one way in which the human brain may arrange certain fundamental necessities of syntax.
The average person will probably be familiar with polysynthesis as the mechanism whereby, in Western stories, Indians may have names with immensely long and poetic meanings, like »He-Who-Overleaps-The-Brook-Of-Red-Fish« or some shit. I am not fit to judge the exact extent of the inventions and exaggerations in such stories (although I have to assume there is some amount), but the principle is true.