Twitter has recently introduced a new Communities feature, which has a similar feature set to Facebook Groups, which is very popular. Twitter has said that for now the new feature is invite only and it is due to be launched sometime in the future.
Like Facebook Groups, Twitter Communities are forum like areas for people to go and discuss things they are mutually interested in, be it motorcycles, Apple or anything. Twitter Communities will be self moderated too and each community can have unlimited members.
If you are interested in starting a Twitter community, you can express your interest here.