A missionary was a member of a religion who traveled to various locations for the purpose of carrying out tasks in furtherance of their belief system, or to serve the community. This might include performing medical care.
James T. Kirk, having traveled to 1930s Earth, explained Spock's appearance to a police officer by claiming it was the result of surgery performed by an American missionary in China, who happened to be a skilled plastic surgeon, following Spock's mechanical rice picker accident. (TOS: "The City on the Edge of Forever")
In 2366, Q, having been rendered Human by the Q Continuum, 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")