I guess she uses "keep" and "keep on" for rhytmical purposes)

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! :)

"Keep" can mean several things. Keep can either be possessive or it can mean to continue something. "Keep on moving" and "Keep climbing" mean to continue "moving" and "climbing" in their figurative sense relatively. "Keep the faith" means to not lose faith and to still believe.