All else being equal circuit breakers can have different "breaking capacity" - it's the maximum current which the breaker can disconnect and it's typically several thousand amperes. The idea is that after that the electric arc can start inside the breaker and it will continue conducting current even with contacts moved apart.

Now how important is the actual value? Suppose I'm shopping for a 20 amperes breaker for my apartment. The retailer offers models with breaking capacities of 1,3 kiloamperes, 3,5 kiloamperes and 5 kiloamperes and higher breaking capacity comes for higher price. Do I always choose the highest breaking capacity? How do I make my choice?