A saturated fat has the maximum number of hydrogens attached to its carbon backbone, ie. there are no double bonds between carbons. When the carbon chain is saturated, it makes a regular zigzag shape and stacks easily with other saturated fats, thus the fat is solid at room temperature. If there is a double bond anywhere in the chain, it straightens out the zigzag at that spot, and puts a "kink" in the chain, preventing the chains from stacking as easily and making the lipid an "oil" meaning it is liquid at room temperature.
The melting point of a lipid is increased by saturation.
A lipid can also be polyunsaturated, ie have multiple double bonds.