2004 Volkswagen Golf ESP light

what is the problem my car shows ESP LIGHT

Your owners manual will tell you what the ESP light is and what it means when it is on. I googled this;

ESP (Electronic Stability Program) is an additional function to ABS (Anti-Locking Braking Sytem) and TCS (Traction Control System). Whereas vehicle fitted with just ABS & TCS will have the ability to prevent the wheels from locking or spinning completely during harsh braking or accelerating.

If the light is on when the engine is running and the car i stopped, it means the car needs service. Specifically the ESP system.

When these lights go on I’ve learned to also check the condition of the battery and its connections. For some reason they do go on sometimes when the voltage is low.