By the end of The Great Gatsby, Nick has emotionally burned himself out. After the tragic events that led to Gatsby's death, Nick has done everything he knew to do to try to get people to come to Gatsby's funeral. While alive, Gatsby was the toast of the town, in death he is forgotten. Everyone used Gatsby for his money and the parties he threw, yet when he was gone, no one wanted anything to do with him. Everyone seemed to forget who Gatsby was. Nick is heartbroken at the way people seemed to forget Gatsby and show their true colors.
There is not much mentioned about the obscenity that is written on Gatsby's front steps, or why Nick erases it. We are left to our own devices to figure this one out. I think Nick was trying to make things the way Gatsby would have wanted them.
On the last night, with my trunk packed and my car sold to the grocer, I went over and looked at the huge incoherent failure of a house once more. On the white steps an obscene word, scrawled by some boy with a piece of brick, stood out clearly in the moonlight, and I erased it, drawing my shoe raspingly along the stone. Then I wandered down to the beach and sprawled out on the sand.
Nick was trying to erase the events of the summer. He wanted to erase what had happened to Gatsby, wanted to erase what happened with Jordan, wanted to erase what happened with Gatsby and Daisy, and I think in some way he wanted to erase that he had even met Gatsby.
The significance of rubbing out the obscene word is open to interpretation. It could symbolize the nature of Gatsby's existence. His identity was constructed, remade. Gatsby was made possible by erasing James Gatz. "Vanishing" is a consistent theme in The Great Gatsby. The dream of Daisy is erased for Gatsby. He subsequently spends the rest of his life trying to reclaim her. He temporarily triumphs and then loses her again. Then he himself is erased in his death.
The erasure is symbolic of all these "vanishings" but maybe it is most symbolic of Nick's urge to erase all the bad memories of Gatsby: the corruption, bootlegging, and the lying. He symbolically erases all of the bad things about Gatsby, leaving only the memory of Gatsby (or Gatz) as the innocent dreamer.