There is a subtle difference.
Keep climbing, keep moving, keep eating, keep exercising are all examples of telling a person to continue to do something. When you add "on" after keep, it stresses the continuation even stronger.
Americans use it sometimes similar to a cheer (cheering people "on".) "Keep on Keeping On" is a popular phrase and basically means to never stop (continue forever).
Summary: "Keeping on" is "keep" x 10. :)
Hope this was helpful! :)