Phi Kappa Phi and Phi Beta Kappa are the two most prominent and well-regarded multi-discipline honor societies, although the latter would likely edge out the former were they to go head-to-head because it is twice as old and established. Phi Kappa Phi is the oldest all-discipline honor society at over 100 years old (Phi Beta Kappa is over 200 years old!), and was the fourth (by some counts the third) honor society established. Association of College Honor Societies: Historical Information
Phi Kappa Phi is by invitation and limited to the top 7.5% of juniors and top 10% of seniors and grad students. Selection is not by GPA, and some chapters are more selective than the organization's general class-rank rule. Membership is extended by invitation (not application), is very selective, and
In many cases, Phi Kappa Phi is more selective than a discipline specific honor society (philosophy [Phi Sigma Tau] or education [Kappa Delta Pi], for example). Discipline-specific honor societies vary on their selectivity and invite-only status and need to be considered independently. For most legit honor societies, you pay once for initiation (pays for induction ceremony, pin, certificate, one-year publication subscription, scholarship fund, etc.) and then future payments are optional, even though you retain membership status. If you want to continue to financially support the organization and its mission, you keep sending money. Otherwise, you don't.
Each society has its own particular benefits, but in general there are several reasons to join an honor society: looks good on a CV, you can get involved with organizing and promoting scholarly activities on campus (speakers and conferences), become eligible for fellowships and other monetary awards, help carry on the tradition of recognizing those who achieve academic excellence, and it helps you remember in those more trying times that someone thought you had a spark of genius in you and recognized you for it.
Honor societies exist to recognize and promote academic excellence, and your membership is like membership in any non-profit organization. You can be on the passive end, just accept the invite, put it on your CV (or hang the cert. on your wall) and forget about it; or you can be on the more active end, join in on the action, take ownership of your membership, and help the organization achieve its mission.
Regardless, Phi Kappa Phi is legit, and regardless of whether you decide to join you should be congratulated on your achievement.