A saturated fatty acid has the maximum possible number of hydrogen atoms attached to every carbon atom. It is therefore said to be "saturated" with hydrogen atoms, and all of the carbons are attached to each other with single bonds.
In some fatty acids, a pair of hydrogen atoms in the middle of a chain is missing, creating a gap that leaves two carbon atoms connected by a double bond rather than a single bond. Because the chain has fewer hydrogen atoms, it is said to be "unsaturated." A fatty acid with one double bond is called "monounsaturated" because it has one gap. Fatty acids having more than one gap are called "polyunsaturated.