An actual leech is a semi-parasitic animal. There are no leeches in The Scarlet Letter, so the chapter title "The Leech" serves as a metaphor.
Real leeches have a dubious reputation. They are jawless relatives to earthworms, and some are slimy and found in swamps. Most memorably, they are capable of latching onto a larger animal such as a human and sucking blood out of it. However, they were historically used for medicinal purposes as well, owing to ancient Greek misconceptions about the role of blood in the human body. The word "leech" is derived from a Latin word meaning "physician", but owing to their bloodsucking ability, the word has become a synonym for a person who behaves parasitically, i.e. profits through harming others.
"The Leech", as a chapter title, is referring to such a person; Roger Chillingworth. Ostensibly this is because of the original Latin meaning of the word, i.e. doctor, because Chillingworth has disguised himself as one. However the double meaning is revealed through Chillingworth's inhabitance with and "care" for Dinnesdale, implying that Chillingworth has attached himself to Dinnesdale and is metaphorically sucking the life out of him;
[Dinnesdale] was haunted either by Satan himself, or Satan’s emissary, in the guise of old Roger Chillingworth. This diabolical agent had the Divine permission, for a season, to burrow into the clergyman’s intimacy, and plot against his soul.