Reason behind more Reactivity of Unsaturated Hydrocarbons
The unsaturated regions are electron-rich and typically allow for electrophilic attack, such as by halogens or protons. Saturated hydrocarbons usually react only with radicals (radical halogenation). C-H activation is often hard in saturated hydrocarbons.

While double and triple bonds are stronger than a single bond when looking at complete cleavage of a bond, one notices that the bond strength of a double bond is less than twice the bond strength of a single bond (with other factors being comparable, there are surely some exceptions). When a double bond reacts, it typically is changed into a single bond, not fully cleaved. Similar arguments hold for triple bonds.