Parasites
The parasites are much like their name implies. They are a wormlike species that need a host to survive. They enter their hosts through their ears or noses and squeeze their way into their brains, killing the host and taking over the host's body. It's never explained in the series, but I think that the parasites gain information from their host's brain, because they function as humans. Some of them (like Reiko) take on the life that their hosts once had. Once a parasite has made contact with a brain, it receives a signal to kill and eat the species it's controlling. It's how the parasites survive, and to some of them, there's nothing more than that; they feel it's their purpose, but is it really? Reiko is a parasite who explores the question.
There are some traits and abilities the parasites have that are important to understanding their part in the series. Reiko has them, and so does Migi, the parasite that is Shinichi's right hand. The first is their ability to sense another parasite within 300 meters from them through brainwaves. This helps them locate allies and enemies quickly. Reiko later states that the signal parasites emit the strongest is bloodlust and hostility.
Another ability that the parasites have is the ability to change. If a parasite successfully took over a host's brain, then the head can change shape. They can take on another face, or become a mass of weapons. They use the latter shape to not only kill and eat, but to battle other parasites if the need comes up. Their instinct is to kill anything they perceive as a threat, and for the most part, anything different from them is a threat, like Shinichi and Migi. Since Migi took over Shinichi's hand, Shinichi's hand can change and distort like Migi wants or needs it to. A parasite's strongest desire is to survive, and they will do anything to make sure they keep on living.
Parasites are extremely fast learners, but most of them are not as studious or as naturally curious as Reiko. Regardless, they are able to pick up math and science concepts quickly, but barely understand human nature or emotions. Their faces are mostly seen as lifeless because they don't know how to convey emotions.
Most people assume that the parasites are alien because they fell from the sky. Admittedly, I first thought they were alien, too. In one of the Parasyte volumes I own, however, there is a questions and answers section in which the mangaka clears it up for us. I thought it was pretty interesting, so I decided to type it up for you here:
Almost every write-up of the series has said so (that they're aliens), but if you actually read the narration, they were intended to have been created somewhere on the Earth. But since they did fall from the sky, I can see why people thought that... but they were just being carried by the wind. When I thought them up, I decided they should be carried like dandelion seeds. But then again, I first started thinking about this story long before I started working at Kodansha... almost ten years ago now, so the exact details are a little fuzzy.