As others have said, the Rotary Club is a group of business owners within a community that come together to serve the community. They are not a secret organization, their meetings are open, and they don't have any secret handshakes. They are not affiliated with any religious organization. It's just a group of business owners coming together to help others.
My boyfriend was able to go to Japan for six months as an exchange student while in High School, due to a Rotary Club scholarship.