We went through this with my son a few years back when he was about the same age as your son. We had a few major changes that had happened in our life at the time: less time with us and more time with a baby sitter due to work schedules, recently moved, new baby brother. Aside from the nail biting, we saw other changes in his behavior such as more defiance and crying.
We made a few changes in our life that allowed us to spend more time with him, after which we saw drastic improvement with all the behavioral issues he was having. It also made the nail biting stop completely.
I'd say that this is mostly just a stage and will likely go away in 6-8 months. But see if there are any stressful changes in his life that you could somehow improve. If not, try to spend more time with him.
Also, kids copy like crazy, so don't model bad behavior by biting your nails in front of him. Make sure no siblings or caretakers are doing it either.