What special responsibility did the Levites have?
We read about the Levites in the Old Testament or the Hebrew Bible; it depends on your perspective. They were one of the twelves tribes of Israel and they had many responsibilites that set them apart from the other tribes. Unlike the other tribes, their chief responsibility was to take care of the tabernacle and later the temple when it was built. So, they took care of the sacrifices, the holy instruments, and the things that were associated with the worship of God.
They also were the priests of the Israelites. They took care of all the major religious functions of Israel. When we keep in mind that there were many festivals, they had a lot of work to do. The high priest was also a Levite. When the temple was destroyed finally in 70 AD, their function change a bit and they focused more on their sacred text.