Mutualism is when two organisms work together and benefit eachother in the process. An example of this is the relationship between the Sea Anemone and Clown Fish. The Sea Anemone provides shelter for the Clown Fish, as the Clown Fish is immune to the Anemone's stings, protecting it from other animals. In return, Clown Fish lures in bigger predators for the Anemone to consume. Thus, both benefit from the relationship.
Commensalism is where one organism benefits from the relationship, but has no impact on the other organism. An example of this is Moss on a Tree. The Moss is away from other organisms who might consume it and also gets more light on the Tree than it would on the floor of the forest. The Tree doesn't get anything out of the relationship, making their relationship a Commensalist one.
Parasitism is where one organism benefits at a detrimental effect on the other. An example of this is a Leech on a Human. The Leech sucks the blood of the Human to feed, thus benefitting in the relationship and the Human loses blood, which is detrimental. In a small amount of cases Leeches have been known to transmit pathogens to Humans, but only several reported cases of this have ever been reported.The Evolution of the Parasite is closely linked to that of its Host, because if the Host were to evolve a way of defending itself against the Parasite then the existence of the Parasite is threatened. Therefore, the Parasite has to either Evolve too, or Die off.