What is the significance of stall speed
There is not one stall speed, instead there are several, depending on aircraft configuration and flight conditions. They are used to determine speeds for the safe operation of the aircraft or for limit speeds.

For example: The stall speed in landing configuration and level flight with the actual weight is used for determining the approach speed. By multiplying with a safety factor of 1.3, you arrive at the recommended approach speed. Or: The stall speed in take-off configuration is used for determining the rotation speed. And so on.

Another example: The speed range in which it must be safe to deploy flaps is limited by 1.4 times stall speed of the clean aircraft, or 1.8 times the stall speed in landing configuration, whichever is greater. Or: The maneuvering speed v$_A$ is calculated by multiplying the stall speed of the clean aircraft with the square root of the maximum allowable load factor. And so on.

If you wonder what a stall is, maybe it helps to read the answers to this question. It is not flow separation or exceeding a specific angle on the control surfaces that determines the stall condition, but the reversal of the lift curve slope over angle of attack: Stall is when more angle of attack will no longer increase lift, so it is the angle of attack of the whole aircraft that counts. Physically, this means that large-scale flow separation appears over part of the wing. A good design will still have fully working control surfaces at this point.