(noun)
a mark, incision, or indentation made into an edge/surface, usually for a particular purpose, for example for securing something or to serve as a record of something;
e.g. There is a notch at the end of the table, made by the chair repeatedly hitting it.
(noun)
a step, degree, or point on a scale, often a figurative scale;
e.g. She hopes to increase her chances of success by a notch or two.
(noun)
a mountain pass that is deep and narrow with close-set walls;
e.g. The road they took ran at the bottom of a notch high in the mountains.
(noun)
to make cuts or slits in something, often in order to mark or secure something;
e.g. She used a saw to notch the shelf so she had a place to hang her tools.
(verb)
to achieve or score something, or to make a record of something by making a mark or cut;
e.g. Next month, she will notch up five years since joining the company.