If you are merely curious what is the meaning of these words I wil try to make a reply.
Gaudiya Math is the preaching institution originally created geographically in India by Srila Bhaktisiddanta Sarasvati Prabhupada. By the dedication and surrender of his disciples and followers and their disciples and followers it now extends outside of India as well. The heads of the various Gaudiya Math temples are mainly to be found to be either the Godbrothers of our A.C. Bhaktivedanta Swami Prabhupada or the disciples of Srila Prabhupada's Godbrothers.
GBC is an anacronym for Governing Body Commision as a group or Commissioner in reference to a singular member. Srila Prabhupada created this commitee of senior devotees within the ISKCON institution to (in theory) as a group oversee the welfare and integrity of the preaching within the ISKCON movement.
Ritvik is the theory that one can be initiated by a Vaisnava who has departed from our earthly vision through an intermediary representative.
If the question you pose also desires an explanation of the apparent controversies connected to these three subjects, that I haven't the time or patience to even try to superficially explain.
I will say that if somehow you have little or no exposure to the fights surrounding these subjects, consider yourself extremely lucky.
Please go on chanting Hare Krsna, read the satras recommended by the Gaudiya Vaisnava Acharyas and try to seek out like minded souls to share the beauty and nectar to be found in such endeavors.
I am not as fortunate as you. I instead have been exposed to the detailed complications surrounding these three subjects and I assure you the better use of investigative energies is to search out how to assist and serve Krsna's servitors to the fullist extent of one's ability.
Gaura Haribol!