What is the reason for using a 10kA breaker rather than a 6kA in simplest possible way possibly with an example?

Breakers are designed to open when there is too much current. For instance, if you have a 100A breaker and you put a 120A load on it, it trips.

But what if you drop a wrench or piece of pipe across the wires? Much more than 100A will flow, usually thousands of amps. This is fault current. If the current is too high, the breaker can weld itself closed and fail to trip. This would be very bad.

So, breakers have an interrupt rating. It indicates how much fault current the breaker can safely handle and still operate properly. Your 6000A or 10000A is the interrupt rating.

You would need a 10000A breaker instead of a 6000A breaker if the fault current could be in excess of 6000A, but less than 10000A.

How much fault current can flow in a given situation? It depends on how heavy-duty the utility distribution transformer is, and how big the supply wires are. The utility company can usually supply the information which an electrical engineer can use to calculate the interrupt rating needed. The whole panel, not just the breaker, must carry the same or higher interrupt rating.