Date: Sat, 11 Jun 1994 21:00:26 -0400 (EDT)
This came up in a class I taught last semester. You can find the actual text of two thirteenth-century consolamentum rituals in Walter L. Wakefield and Austin P. Evans, _Heresies of the High Middle Ages_ (New York: Columbia University Press, 1969), doc. 57 a & b. As both show, the simplest way to explain the consolamentum is as a species of spiritual baptism, given by the imposition of hands and through the holding of the Gospels above the head of the believer.
That is the short answer. The truth seems to be that the consolamentum changed greatly over the course of Catharism--it is not even attested among the Orleanists, who are thought by many to be the earliest known Cathars or proto-Cathars. There were also probably minor variations between the different sects of Cathars--of which there were several in France and Italy.
Evans and Wakefield note that the ritual freed the person receiving it both from their personal sins, and from the "sin committed at the fall from heaven." (p. 465) This allowed him or her to pursue release from earthly existence and reincarnation. In order to be given the consolamentum, the supplicant had to have undergone a strict probation to show himself or herself worthy.
I suppose that it was a consolation or comfort in the same sense that baptism is. The Latin might also allow us to read it as an alleviation or relief, perhaps from sin or from the bonds of incarnation.
The consolamentum might be given more than once in a life time, and, in fact might be repeated if necessary. It seems to have been as important for those conferring the consolamentum to remain pure as for those who were receiving it.
There are questionable references in Catholic sources to the endura, which was supposed to follow the consolamentum for those who did not wish to live life as perfecti. (Perfecti were Cathars who lived a spiritual existence involving abstinence from sex and all animal products; they often formed a class of wandering clergy.) In the endura, the consoled Cathar was supposed to take no food, and starve to death. In this way, they would commit no further sins. This is not attested in early Catharist sources, but, it does appear to have been a practice among the late (and extremely peculiar) Cathars of Montaillou in the fourteenth century. Much in their beliefs and practices is unusual, and although Emmanuel Le Roy Ladurie's account, _Montaillou_, is perhaps the most widely known work on the Cathars, neither it, nor the heretics it describes can be taken as typical.
I hope this helps.