Double bond configuration (cis vs. trans). In a trans orientation, the hydrogens on the carbons involved in the double bond are opposite of one another. In the cis orientation the hydrogens are on the same side of the bond. Steric hindrance in the cis orientation causes the chain to take on a more bent shape. As a result, the melting point is much lower for cis fatty acids compared to trans and saturated fatty acids.
If an unsaturated fatty acid is completely hydrogenated it would be converted to a saturated fatty acid. However, this isn't/wasn't always desirable, thus partially hydrogenated vegetable oil became widely used. It makes it more shelf stable, because the double bond(s) of unsaturated fatty acids are susceptible to oxidation, which causes them to become rancid. Partial hydrogenation causes the conversion of cis to trans fatty acids.