I think it's often a personal thing, worn for the same reasons that medieval knights displayed a coat of arms and people in Japan still have mon badges printed on their kimono - to make it easier for people to recognise you, to show your allegiences, and give people an idea of who you are.
Since they wear helmets most of the time on the battlefield, Mandalorians would have to rely on crests to recognise and form opinions about allies they've never met before. You'd know that a guy wearing a jaig crest is probably going to be highly skilled, and the guy with the crosshairs crest has probably got a decent aim. A leader dealing with squads he's never worked with before would have an easier time deciding what he wants everyone doing.
Family and clan/group crests would make is easier to know who's with who and who's related to who. It's rather morbid, but it would also help sort out the dead after a battle.
In the real world, crests sometimes have something to do with names. Even today, the Mitsubishi company uses the Mitsubishi family's mon of three diamonds. 'Mitsu' is Japanese for three, and 'bishi' is diamonds.
Inspired by this sort of thing, my Mandalorian character wears a mouse becuase her Theelin surname (Equiqua) sounds like 'Little Eek' in Mando'a (Eki'ika).
Crests can also be tied in with personality quirks or exist solely as art. In real life, this is very evident in Japanese kabuki performers. The Onoe line (pronounced 'o-no-eh', not 'oh no'...) encouraged people to pay attention to their performances with a design of 'listen carefully' - 'yoki koto kiku' in Japnese - with a design consisting of an axe (yoki in Japanese), a sort of musical instrument called a koto, and a crysanthemum (kiku).