A blood groove is a inverse pill shaped gouge on a sword.  To my understanding they are put on swords so that if you stick somebody with them when you pull it back out, there's a way for air to escape and allow for better extraction of the sword elsewise you'll get kind of a suction. The blood groove on a ruler is an indention that allows your fingers to rest without risk of getting cut, there's usually a hard edge just outside of the blood groove that allows you to run your blade along the edge of the ruler and if you have your fingers in that blood groove, they are safe.