All three are forms of symbiosis--a relationship between two kinds of organism.
A parasite (think tick, mosquito, or tape worm) benefits from the relationship while the host is damaged. The parasite munches on you or steals your food, but either does not kill you or kills you rather slowly, bit by bit.
A commensal benefits from the interaction, but the host is not hurt. For example, ants living near your compost heap may prey on insects attracted to the compost, but you are not injured by this.
In mutualism, both organisms benefit. The bacteria living in your intestines benefit from the food you eat and most of them also help you digest food, produce vitamin K and other things not yet fully understood. Mice raised with no intestinal bacteria need 30% more food than normal mice with intestinal "flora."
Check out
Wikipedia for more information.