While the synagogue was a place for prayer and study of scripture, the Temple was a place for sacrifice. Just as sacrifice of animals is always a part of religion in the ancient world, it played an important part of the practice of religion in Jerusalem.
Judaism differed from other pagan religious ceremonies in some very important ways. For example, unlike Greco-Roman religions, there is only one place in the world where and acceptable sacrifice can be made, the Temple at Jerusalem. This was not always the case for the Jews, even as late as the reign of Hezekiah in the 8th century B.C. there were still local shrines where sacrifices to the Lord were made. Hezekiah attempts to reform this system with limited success. In the post-exilic period there are several examples of competing temples in Egypt (at Elephantine and Leontopolis).
Jewish sacrifices were more expensive than Greco-Roman sacrifices primarily because there was a class of priests who needed to be supported by the populace. There was no professional priesthood in Greece or Rome, anyone could function as a priest (Alexander the Great and the Caesars, for example, were priests). Priests in Israel were hereditary and were prohibited from working to support themselves outside of their role as priest. See this previous post on the wealth of the Temple.
The Temple was central to the life of the “common Jew.” As N. T. Wright puts it, “At the heart of Jewish national life, for better or worse, stood the Temple” (N. T. Wright, Jesus and the Victory of God, 224). The impression one gets from reading the more extreme views of the Essenes or Jesus’ sharp critique in the New Testament is that the Temple was viewed negatively in the first century. Despite politically ambitious High Priests and possible corruption in the first century, most Jews supported the Temple through offerings willingly given. Diaspora Jews even supported the Temple through the half-shekel “Temple Tax,” a practice the Romans required to be continued after the revolts, although the money was diverted to Rome (War 7.218; Dio Cassius, 66.7).
Sanders warns us it is possible to have too positive of a view of the Temple based on Josephus (a priest), Philo (a pilgrim, in this case) and other early writers (Judaism, 54). There were wealthy, powerful priests and others who lived in poverty. The critiques of the Temple by the Essenes and the Gospels may therefore be taken as a corrective to the positive material in the Jewish sources.
Yet in the New Testament the Temple is impressive to the Disciples (Matt 24:1-2) even if the current leadership is under God’s judgment and about to be replaced (Mark 12:1-12). It is still the main place for the apostolic preaching in Acts 2 and 3, although by Acts 7 Stephen is accused of attacking the Temple. Both Paul (Eph 2:19-22) and Peter (1 Peter 2:4-5) refer to believers as stones in a living Temple.