Most people who join lineage societies do so for the prestige of being able to prove their pedigree. A lot of research goes into lineage society applications, so you know when you are accepted into one, you really are descended from a prestigious, prominent, or famous person. It gives you bragging rights on your family tree, and that’s a very enticing thing.
It’s not just prestige that gets people to become interested in joining lineage societies, however. Some societies have genealogical libraries that are only open to members (or only open for free to members). The opportunity to network with other people who have similar ancestry to you is also nice. There is also a very strong possibility of you meeting a genetic relative in a lineage society (someone who is descended from the same person as you), which gives you the opportunity to exchange family information, and maybe even discover new family artifacts, documents, records, and photos that you never knew still existed.
Other reasons for joining a lineage society include bringing awareness to the particular group or time in history that the society celebrates, participating in the society’s charitable endeavors (some engage in charity and public service, while some do not), getting that coveted membership certificate for your wall, being able to contribute your own genealogy research to the society, the thrill of accomplishment when you are accepted as a member, and the opportunity to get out and socialize with people of similar interests to yours at meetings.