The light-colored stones are part of a 4th century (CE) Synagogue (sometimes called the "White Synagogue"), which was built on the black, basalt foundation of a previous synagogue which would likely have been standing in the time of Jesus (sometimes called the "Synagogue of Jesus").
Many people believe this older synagogue is the one referred to in books Mark (1:21) and Luke (4:31) of the New Testament.