Mark 1:21–28 (ESV)
21 And they went into Capernaum, and immediately on the Sabbath he entered the synagogue and was teaching. 22 And they were astonished at his teaching, for he taught them as one who had authority, and not as the scribes. 23 And immediately there was in their synagogue a man with an unclean spirit. And he cried out, 24 “What have you to do with us, Jesus of Nazareth? Have you come to destroy us? I know who you are—the Holy One of God.” 25 But Jesus rebuked him, saying, “Be silent, and come out of him!” 26 And the unclean spirit, convulsing him and crying out with a loud voice, came out of him. 27 And they were all amazed, so that they questioned among themselves, saying, “What is this? A new teaching with authority! He commands even the unclean spirits, and they obey him.” 28 And at once his fame spread everywhere throughout all the surrounding region of Galilee.
The synagogue can be thought of as a local church for the Jewish community. "It served primarily as a location for the reading and teaching of the Law of Moses, but it could also function as a place for prayer, for the education of children, and for community events. During Jesus’ time, every significant Jewish community in Galilee had a synagogue." Lemke, S. W. (2007).The Academic Use of Gospel Harmonies
The synagogue was not to be confused with the temple. There was only one temple in Jerusalem where the sacrifices were offered and the primary religious activities took place. The synagogue was not meant to be a microcosm of the temple or really even resemble it. It was simply meant to be a gathering place for Jews that lived away from Jerusalem.
The Jews met together at the synagogue on the Sabbath day. The Sabbath in the Jewish calendar is from sundown Friday evening to sundown Saturday evening. There were strict regulations that the Jewish religious leaders required of the people in order to keep the fourth commandment ("Remember the Sabbath day by keeping it holy. Exodus 20:8) We will address these in more detail when we come to the end of chapter 2 and the beginning of chapter 3 where Jesus challenges those strict regulations. For now, it's important to know that the Sabbath is a day for stopping and resting from work to look back to God's creation activity in Genesis 1 and the rest of entering the promised land, also to look forward to his recreation and fulfillment of his promised coming kingdom. On the Sabbath the people would stop from their work and gather together to read the Torah and trust in the provision of God.