A long-chain carbon compound with many unsaturated bonds. An 'unsaturated bond' is a double bond between two carbon atoms; this could become a single bond, with the 'extra' bonds holding some other atom, usually a hydrogen.
If the carbon atoms are completely filled, the compound is saturated, if there is only one bond 'free' it's called Monounsaturated. Usually these terms are used in relation to 'fatty acids', oil, butter, etc. Saturated fatty acids are usually solid at room temperature (Margarine), while polyunsaturated are liquid at room temperature. Polyunsaturated fats are good for reducing cholesterol.
H H H H H H H H
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--C-C-C-C-- -=C-C=C=C-C=C-C--
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H H H H H H H H H H
Saturated Polyusaturated