Hot water helps the cleaning process (i.e. moving the dirt from the object being cleaned to the water) because it can dissolve the dirt faster and break strong bonds (up to a limit, of course) of dirt with the item being washed.
It is worth mentioning that between the detergent and the hot water, the detergent contributes more to the dissolution of dirt in the water than does hot water alone (that is the same reason it is better to wash your hands with soap and water than with water alone). However, for optimal results, using both detergent and hot water will clean better (and faster).
The detergent (or soap) is actually what is called a surfactant which are chemical compounds that decrease the surface tension or interfacial tension between two liquids, a liquid and a gas, or a liquid and a solid.
Not to be overlooked is the action of scrubbing which greatly assists in the removal of the oils and dirt by exposing more of the surfaces of the molecules allowing the surfactants to work faster.
I hope this is helpful.
Craig