The Mayor symbolizes the corruption of small-town Russian life. It is he who has the most to lose by the inspector's imminent arrival. He's petrified that all of his corrupt dealings—all the bribes, the graft, the backhanders—will be ruthlessly exposed to the full glare of publicity. So the Mayor takes an active role in trying to clean up the town—in both senses of the word—at least temporarily.

But of course the so-called inspector is no such thing, so all of the Mayor's manic efforts to clean up the town and hide his numerous shady dealings are all to no avail. The suggestion here is that the rampant corruption at the rotten heart of Russian civic life cannot be expunged quite so easily. For that to happen, those responsible for this permanent blight on society such as the Mayor will need to own up to their transgressions and be held to account for them. And this will only happen when the real government inspector arrives.

The mayor is the leader of the group of officials that run the small Russian town, all of them corrupt.  He, along with the rest of them, are terrified at the news that an inspector will soon be coming to their town to check things out.

In many ways, he plays the dupe after Khlestakov arrives and they mistake him for an inspector and do anything he asks including loaning him huge sums of money.  After they find this out, the enraged and incredibly humiliated mayor also finds out that the inspector wishes to see him.  Immediately.