These are all terms used when talking about the steps toward conversion. Here are brief explanations.
Brit Milah is a Jewish religious male circumcision ceremony performed by a mohel (who can also be a urologist) on the eighth day of a male infant’s life or before a man converts to Judaism. At Darshan Yeshiva, students are required to arrange this on their own. Darshan Yeshiva does not provide this as a service. Students work with their rabbi to provide the best option available to them. If a male is already circumcised, a ritual drawing of blood called hatafat dam brit can also be performed where a tiny drop of blood is extracted from the penis.
Bet Din is a three-person panel who meets with the student prior to their conversion to Judaism. This is often three rabbis (your rabbi plus who others) but does not have to be. The bet din symbolically “authorizes” you to convert to Judaism and be accepted among the Jewish people. A bet din will ask you questions such as “what is your favorite holiday” or “why are you interested in converting to Judaism?” The bet din is not judging you, nor is being with a bet din an uncomfortable ceremony. It is not like defending yourself in court. It is a friendly exchange of ideas prior to mikvah.
Mikvah is a ritual bath. This is where Christians get the practice of baptism. A mikvah is any kind of moving, “living” body of water such as an ocean or lake. More commonly a mikvah is a small pool, usually inside a building like a synagogue. Mikvah can include a person who assists you through the process, or it can be done completely private. Both approaches are valid for conversion.
Students who wish to join more traditional synagogues (Conservative, more traditional Reform and Reconstructionist communities) should participate in all the above rituals, as they are required by Jewish law.
Conversion certificates are signed by the rabbi who facilitates your conversion. Every student receives one. We’re often asked “is my conversion certificate valid?” A conversion certificate is not like a passport or a driver’s license, so there is no answer to that question. Your certificate is a record of your conversion and a symbol of your commitment to Judaism. It is meaningful to you and to your rabbi, as well as any other rabbis or communities you may choose to join in the future. As we do not provide conversion for the sake of moving to and becoming a Jewish citizen of Israel, the question of valid or invalid is irrelevant.