Paramecia is the name given to a type of Devil Fruit. These fruits give the eaters a "super-human" power, usually it affects the eater's body in some way.
Grants the user an ability that can be classified only as 'Superhuman'. The Paramecia fruits also contain the greatest variation of powers evident as they seem to offer the widest range of possibilities when it comes to how to exploit the ability granted to the User. Some people may encounter inspiration for a new attack after using a particular moveset for years while others will never learn how to completely use their skill.
The Paramecia type is the only group containing the powers or special traits that are considered 'useless' to the user, granting little or no real advantage whatsoever. Paramecia types are also the easiest to fight against because while the strengths of their powers give them an advantage, they also make them easy to predict and often their abilities are displayed to their fullest within a very short period of time (as noted by Enel). Although other Devil Fruit types may also leave the user as a "freak", none are more noted for this habit then the Paramecia group, whose powers are often far too freakish for normal people to accept.
Paramecia are the most common of the Devil Fruits types. Paramecia fruits can be divided into several subcategories, as it is impossible to generalize the powers. For instance, Gomu Gomu no Mi and Yomi Yomi no Mi have powers that are active at all times. Others like Noro Noro no Mi and Hana Hana no Mi have powers that need self activation in order for them to use their abilities. They however all seem to come in two basic types. Whatever powers a paramecia fruit gives, it is based on the concept of either a characteristic like slipperiness or slowness, or an object like a bomb or a door.