Final answer:
The green SOV CLOSED light on APU control panel and the green APU SOV CLSD message on EICAS indicates that the APU shut-off valve is closed.
Step-by-step explanation:
The green SOV CLOSED light on APU control panel and the green APU SOV CLSD message on EICAS indicates that the APU shut-off valve is closed. This means that the APU shut-off valve, which controls the flow of fuel to the APU, is currently closed. It does not indicate whether the APU is running efficiently or malfunctioning, or if the APU cooling system is operational.