A molecule with a long chain of carbons bonded together and flanked by hydrogens with an acid group on one end and a methyl group on the other end is called a fatty acid.
A fatty can be saturated as well as unsaturated. Saturated fatty acids are the ones that do not have any double or triple bond in them. Unsaturated fatty acids are the ones that have double bonds or triple bond in them.
Some of the examples of fatty acids are stearic acid, palmitic acid, linoleic acid etc.
Some common examples of food products having fatty acid in them are walnuts, fish, butter, milk etc.
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