Burr knots are root initials that develop above ground. Rootstocks are selected for their ability to produce roots, but some rootstocks try to produce roots above the ground. The severity of burr knot development differs depending on the variety and region. In several rootstock trials, trees in Virginia tended to produce more burr knots than trees in most other locations. Sometimes several burr knots will coalesce and partially girdle the tree. Burr knots are considered undesirable because they can be a site for disease infection, winter injury, and insect attack. There is little that can be done to suppress the development of burr knots. For more information and images, read this article on Burr Knots on Apple Trees.
Answer provided by Dr. Richard Marini, Penn State University.