Montag's leg gets to be like this after he has killed Beatty. In this episode, the firefighters (with Montag among them) have gone to Montag's own house to burn it down. They are doing this because he has books.
After they burn the place down, Montag kills Beatty. He does this by burning him with his flamethrower. Once Montag does this, the authorities come for him. They release the Mechanical Hound to kill him. The Hound gets him in the leg before he can burn it. That is why his leg is like this.
I believe the leg itself represents the life Montag use to have. When the mechanical Hound shoots morphine into his leg and it becomes numb. It is as though he loses his leg forever. He feels the pain of the leg being lost at that moment. This represents that he is mourning for what he had lost. Montag weeps for the life he loses and will never get back. He feels the "hollowness" that once represented his life and he weeps for that. He then stands up and continues as one would have to keep going after "losing a leg" and having to learn to walk again or in this case losing the lif he once had and having to keep on going.