Mermaids are beautiful human females with a fishes tail in place of legs. They spend the majority of their time underwater, with variations on the myth giving them limited time out of water.
The term mermaid sometimes applies to and human/fish hybrid regardless of the gender or the ratio of human to fish. To distinguish sex the male version is now more often called a Merman.
The stories of mermaids have been with mankind since at least classical times, as is evident from the presence of Sirens in the myths of Homer. The mermaids were somewhat of a natural extension of sailors as the two things they faced most often on their journeys across the seas were loneliness and the water itself. Generally speaking mermaids existed merely as fantasies but in the Middle Ages they were partially reconfigured by the Catholic church as the purveyors of sin. They represented the temptation of women to lead men to their doom, and thus the stories of mermaids turned from playful or benevolent to those who would lead men to their doom. They first seduced them above waters and once they were successful dragged men to the depths. Thus the concept of mermaid as a monster became common in literature as well (this was visible for instance in one of the Pirates of the Caribbean movies.) Despite this the most famous mermaid is the Little Mermaid, a Danish myth. She is portrayed as a creature stuck between two worlds, one who longs for love on land while being forced to stay in the ocean. The story is sometimes portrayed as a cautionary one (sort of along the lines of "be careful what you wish for") and at other times an inspirational one (more along the lines of "true love conquers all'.) The use of the term mermid has not been consistent throughout history either applying to a wide variety of mythical creatures or characters including Sedna, Yemaya, Melusine, the Sirens and the Selkies.
Based on the somewhat loose definition of the term, characters such as Mera, Dolphin and Namorita could also be considered mermaids, as although they are not strictly mermaids, many other characters from myth and fiction are considered mermaids that do not have the exact characteristics of mermaids themselves either.