A missionary was a member of a religion who traveled to areas for the purpose of carrying out tasks in furtherance of it or to serve the community. This can include performing medical care or charitable work.
James T. Kirk, having traveled to 1930s Earth, explained Spock's appearance to a police officer by claiming it was the result of plastic surgery performed by a missionary in China after a mechanical rice picker accident. (TOS: "The City on the Edge of Forever")
Q, after having been rendered Human by the Q Continuum in 2366, sarcastically stated that he would perform missionary work instead of continuing his previous terrorizing ways. Data claimed such work would be "noble". (TNG: "Deja Q")