Harper Lee uses the clock tower in her description of the Maycomb County courthouse to symbolize the fact that Maycomb is stuck in its past and unable to move forward. We especially see the association of the clock tower with the past in the sentence describing the clock tower:
From the other side [of the courthouse], however, Greek revival columns clashed with a big nineteenth-century clock tower housing a rusty unreliable instrument, a view indicating a people determined to preserve every physical scrap of past. (Ch. 16)
In other words, she is describing the courthouse as being designed in early Victorian, or 19th century, but as also having Greek revival columns as well as a 19th century clock tower. The description of Victorian architecture helps portray Maycomb as being stuck in its past, while the Grecian columns portray it as being even further stuck in its past. Finally, the description of the Victorian clock tower holding a rusty clock that doesn't really work further shows that Maycomb is not just stuck in its past but that its insistence on being stuck in the past is really not helping the citizens of Maycomb in the slightest.
Being stuck in the past ties in with Lee's central theme in To Kill a Mockingbird concerning racism, along with all of the injustices and ethical and moral deterioration that go hand-in-hand with racial prejudice. Just like their slave-holding forefathers, the citizens of Maycomb still hold on to their racial prejudices and those racial prejudices are not helping Maycomb to progress into a just, democratic, American society. Hence, Lee is using the Victorian clock tower plus its rusted clock to show just how terrible and socially nonprogressive racism is.