Fatty acids are fats that have acidic carboxyl groups on them. Something like
CH3-(CH2)n-COOH
Unsaturated fatty acids have double bonds between 1 or more of the carbons in the chain. They are unsaturated with hydrogen, but can be hydrogenated chemically.
Fatty acids have many roles, but a very common one is to form the lipids in membranes. In that case two fatty acids are usually joined to phosphate plus some other chemical groups.
