To polish a sentence means to remove unnecessary words or phrases so that the sentence is concise and to the point, instead of being too wordy and hard to follow. I'll try to give an example...
It is commonly believed that John is a an extremely comical and funny boy.
It is believed that John is a very funny boy.
Many believe that John is a funny boy.
The first sentence is wordy, the second and third sentences say the same thing as the first, but in a more concise manner.