Behind it, along the wall, is a stone bench - on which the elders of the city sat. This custom is referred in several Biblical passages. Example (Ruth 4 1-2): "Then went Boaz up to the gate, and sat him down there...And he took ten men of the elders of the city, and said, Sit ye down here. And they sat down".
This photo shows the center of the village from ground level, with the 4th century AD synagogue on the left. On the right side are the Byzantine ruins of the village in the center, which occupied the same area as of the early Roman houses (from the time of Jesus).
Capernaum grew larger at the time of Jesus (early Roman period, 1st century AD), and a synagogue was built in the center of the village. It reached its peak in the Byzantine period when the grand white-stone Synagogue was built (end of the 4th century AD) over the earlier synagogue.