Over the course of the book, Roger Chillingworth's appearance changes drastically. At first, he simply looks like an old man. He is sort of weathered, but he looks pretty normal for an old man.
By the time we get to the end of Chapter 14, he has changed a lot. He no longer looks normal all of the time. Instead, he (at times) looks like a devil with red fire showing in his eyes. He tries to stop this from happening and makes it go away as soon as he can, but it's there.
This is meant to symbolize how far his hatred of Dimmesdale has changed him. As Hawthorne says,
In a word, old Roger Chillingworth was a striking evidence of
man's faculty of transforming himself into a devil, if he will
only, for a reasonable space of time, undertake a devil's