Parasite universes, as the name suggests, are universes that swoop in on bigger worlds (such as the Discworld's) and feed upon them. There is usually quite a strong barrier that prevents them from entering, but this wall noticeably gets weakened during circle time, a period that is marked by the common appearance of crop circles. It is this time that the larger universe is more vulnerable and thus more prone to attack.
The Dancers, a ring of eight magnetic stones, act as another protection against the elves.
The parasite universe mentioned in the book is namely the ones that the Elves inhabit. There were three major times of a weakened barrier - one when young Granny Weatherwax and Mustrum Ridcully were having a love relationship in Lancre, a second time during Granny's old age (which served as the plotline for Lords and Ladies), and a third occuring after Granny's death (plot for The Shepherd's Crown), with the latter two having elf invasions, all successfully battled. There were also mentions of the dark ages long ago, when people lived in fear of free-roaming elves, but that age has long since past.