It means firing at very close range for artillery.

By the First World War, artillery typically fired indirectly, meaning at targets the gun battery itself could not see, from a range long enough that terrain often interfered with direct line of sight. A complex system of communications and observers is what makes this effective.

Even if guns themselves could see the target, say, because of elevated positions, the range would still be long enough that a telescopic sight and ballistic calculations would be essential for accuracy.

"Firing over open sights" is firing at a target so close that you don't need any of that, and can just point the gun tube at the target make crude estimations and fire away. It's generally only done in an emergency, and implies the gun position is in danger of being overrun.

By the way, this question would probably be suitable for the "short answers to simple questions" thread.