1. To give someone's or something's heels little ineffectual bites. Their dog kept nipping on my heels whenever I walked through the house. I know some people go crazy for the treatment, but I can't stand the feeling of fish nipping on my heels!

2. By extension, to be very close behind someone or something in rank, score, ability, etc. This underdog team has been nipping on the reigning champions' heels since the very beginning of the match. As technology has improved and become more cost effective, 3D printing has been nipping on the heels of the traditional crafting and manufacturing processes.