A Purple Smurf is basically a Smurf who has been infected with the "purple disease" by either a purple fly or by another Purple Smurf, usually by biting him or her in the tail.
A Purple Smurf usually hops around with gritted teeth, making "gnap gnap gnap" noises, and searching for his or her next victim.
A Purple Smurf can be cured by inhaling the pollen of a tuberose blossom, causing him or her to sneeze and restoring him or her back to normal.
In the original comic the Purple Smurfs were named Black Smurfs and had a pure black color scheme (save the classic white pants and hats of Smurfs); this was changed to Purple in later works due to concerns of racial stereotyping.
They are a parody of the popular media depiction of zombies, suitably toned down for the child-friendly world of most Smurfs media (though the depiction predates Night of the Living Dead several earlier zombie works existed, such as I Walked With a Zombie, which likely inspired at least partially the creation of the Purple Smurfs).