A Mark is the cut and subsequent scar a Shotet person uses to record a loss. There is some misnomer about this; most believe it records the number of people a Shotet has killed, but it really records the person's loss.
The phrase "carve the mark" is uttered twice in the first novel, first by Cyra, and then by Akos. The ritual involves cutting your arm with a blade, all the while uttering the deceased's name over and over again. When the wound is fresh, you paint it with a special blue dye so that it never quite heals.
If someone dies from natural or accidental causes, a loved one can record the loss with a special hash mark through the original mark, to differentiate it from a kill mark.