A saturated organic compound has general formula C_nH_(2n+2). Halides count for H, and if the formula contains nitrogen, we subtract NH before the determination. Every 2H"'s" less than the saturated formula corresponds to "a degree of unstaturation". And each degree of unsaturation corresponds to either a double bond (i.e. C=O, C=C, C=N) OR a ring junction.
For benzene, the molecular formula is C_6H_6. A saturated alkane with 6 carbons would have a formula of C_6H_14. Thus benzene has 4 degrees of unsaturation. The representation of benzene as "1,3,5-cyclohexatriene" makes these degrees of unsaturation very easy to see.
So aromatic compounds are by definition unsaturated.
