It's a way of adjusting your premiums based on your claim history (usually not your driving record in other respects). A long history of no claims can typically reduce the premium to less than half the base rate, though specifics vary from place to place. A bad history can increase it to more than double the hase rate.

It's usually written "bonus/malus" with a slash, BTW. It's one or the other: a bonus (premium reduction) or malus (increase).

Many countries use this system, not just in Europe. India and Tunisia do, as two random examples.