Usually this means your monitor is turned on, but your computer is not sending it anything to display.
Your computer may have entered a power saving sleep or hibernation mode. To wake a computer from sleep mode you will just need to press a key on your keyboard. To wake a computer from hibernation mode you will need to briefly press the power button. If you are unable to wake your computer using either of these methods it is most likely that the cable from the computer to the monitor is loose or unplugged, check to see that both ends of the lead are connected securely.
Alternatively, if the cables are all secure then there may be a hardware fault. Try a swap test – swap the monitor that is not working with one that is working, you could also try connecting the monitor you suspect is faulty to a computer that is currently working. If you suspect a faulty monitor check with your supplier whether it is still under warranty.