Sa'at means "clock", which refers to

the four face clock in top of the tower.
The Municipality was built in 1934 as the Tabriz municipal central office. After World War II it was used by the Azerbaijan Democrat Party as a Government Office. When Iranian troops regained control of Tabriz in 1947, the building was again used as the Tabriz municipal central offices, a function which has continued up to the present day.
In recent years parts of the building are decorated in function of museum. The museum includes historical maps and photos of Tabriz. There are also some antiques like first taxi cars, old firefighting tracks are shown in the museum.

Since Saat Tower is located in the center of the city, it has been used for various ceremonies and gatherings in the city. During 1947 it was used as the seat of the Azerbaijan Peoples' Government.

Iranian new year, at the beginning of every new Iranian Year (20 March), a big Haft-Sin is made behind Saat.
Earth hour, since 2014 Tabriz celebrate the earth hour by turning off the lights for Saat Tower.

Reference:
http://en.wikipedia.org/wiki/Saat_Tower