When someone has strictness, they make sure that rules are followed and that things are done in a certain way.
Strictness can be good because it helps people behave well, but it can also be bad if it is too much and makes people unhappy.
Examples:
The teacher's strictness helps the students learn.
His strictness about safety keeps everyone from getting hurt.
She shows strictness when she makes sure everyone is quiet.
The strictness of the referee makes the game fair.
The strictness of the law keeps people safe.
The strictness of the librarian makes the library a quiet place.