Purple Lums are a species of non-collectable lums that are used to swing from platform to platform. They are first introduced in Rayman 1. They are said to assure the cohesion of the Dream Glade, and presumably Rayman's World.
Betilla the Fairy gives Rayman the power to swing from them. By shooting a Purple Lum with his magic fist, Rayman can swing from the Lum by an energy rope to reach areas which are too high or too far to reach by jumping alone. It is received directly after defeating Adult Moskito. In this game, the Purple Lums are actually pinkish, with yellow wings. There are reddish types which start slowly falling after Rayman latches to them.
Rayman 2, Ly the Fairy teaches Rayman how to use Purple Lums after freeing her from the Robo-Pirates' prison. Purple Lums are the largest of the Lums. According to the game, no matter would be solid with the existence of Purple Lums.
They also appear in Rayman Arena. Any of the characters in Rayman Arena can grab on to them by shooting at them.
The only exception on Rayman 3 is that a blue Hoodlum superpower called the Lockjaw can give Rayman his power instead of a fairy, and Purple Lums themselves are replaced by metal hooks. It is possible that these are still Purple Lums, just with a different, more machine-like appearance. If this isn't true, however, it is highly likely that Purple Lums have been removed from the series, as the metal rings also appear in the GBA version of Rayman 3, Rayman: Hoodlum's Revenge, and the GBA version of Rayman Raving Rabbids.