A coronet is a small crown which is worn by a nobleman or noblewoman. In the European tradition coronets differ from kingly crowns in that they lack arches—they are instead simple rings with ornaments attached. Different ranks of nobility wear different coronets. For example, in England the various ranks are denoted as follows:
If you bothered counting the “pearls” and strawberry leaves on the above illustrations, you will recognize that certain adornments have been left out (which is to simplify the heraldic representation of coronets). I wish I knew what the strawberry leaves represent! If I was a sinister & bloodthirsty nobleman, that is not the sort of decoration I would choose for my fancy fancy hat, but maybe I am not thinking like a peer. Other western European nations have differently shaped coronets with different ornaments, but the same sort of rank-by-decoration pertains.
Coronets are largely symbolic—many nobles do not even have them made. By tradition they are worn only at the coronation of a monarch. Coronets are important however in heraldry, and the peerage rank of a noble house can easily be determined by looking at the little crown drawn on their shield.