A high-anonymity community doesn’t reveal who people are and perhaps prefers that people do not inadvertently reveal who they are. Such a community allows people to post without bad repercussions coming their way. This is good if a person has controversial things to say and needs cover, but bad if a person intends to do nothing more than disrupt the community.
A low-anonymity community requires people to reveal who they really are, perhaps with real names and real e-mail (or even snail mail!) addresses. This has the positive value of keeping folks from flaming, but it may be too intimidating to those worried about such things as identity theft. Moreover, a low-anonymity community necessarily encourages people to stand behind their own words — this may improve overall discourse.