Parasitism and symbiosis are related biological concepts but they are not to be confused as the relationship between the organisms involved is importantly different. It is the difference between exploitation and cooperation. Parasitism is one organism making use of another. Whilst symbiosis involves organisms working together for their mutual benefit. Fleas and mites are parasites of many animals, simply feeding on them. Some gut bacteria, on the other hand, perform functions that are beneficial to the organisms that they inhabit, including human beings.
Parasitism is a more familiar concept than symbiosis perhaps because of its adoption as a term of abuse for those who sponge off others. In biological terms a parasite is an organism that gains nutrients from another organism, which is its host. It provides nothing to the other organism in return for those nutrients. Some parasites are exoparasites, living on the outside of the host animal, whilst others are endoparasites, living inside the host.
Examples of exoparasites include the ticks and fleas that cause such a problem for so many pet owners when their animals are infested. Tapeworms, on the other hand, are an example of an endoparasite. Parasites can be faculative (able to switch between alternative lifestyles) or obligate (tied to one set of conditions). They can also have widely varying effects from being a mild drain to causing the eventual death of the host.
Symbiosis is a less well-known concept than parasitism. Sometimes when an organism lives in or on another creature it can look very much like a case of parasitism. But it could, rather, be a case of symbiosis. It may be that whilst the organism is receiving something useful from the other organism, it is also giving it something back as well. When this occurs the result is known as symbiosis and the organisms involved in the arrangement are symbionts.
An example of symbiosis is the case of gut bacteria in many organisms including human beings. Indeed, in humans, it has even spawned products such as yoghurts that are aimed at boosting the gut bacteria that are thought to be useful. Various good properties of these good bacteria of the gut flora include aiding digestion, the prevention of allergies, fighting off harmful bacterial species in the gut, fighting inflammatory bowel conditions, and helping useful cell growth. Species in symbiosis will often evolve together in a process known as coevolution like in the case of insects and flowers.