The placement of multiple machine guns so that their paths of fire cross, like this:
\\ / \\/ /\\ / \\ / \\ (gun) (gun)The advantage of setting up machine gun emplacement like this is that no one can cross the lines of fire as it is difficult to find cover from both guns. When multiple crossfires overlap, the machine guns provide each other with mutual protection, and it is theoretically impossible for infantry to reach the guns. Tanks, airplanes, and crawling along the ground are all effective counters to a crossfire by itself. When combined with land-mines, snipers, barbed wire, and air cover, crossfire became a difficult tactic to counter in the early 20th century.
Crossfires were first used in World War I, shortly after the invention of the machine gun. The guns were placed in groups, called machine gun nests, and they protected the front of the trenches. Thousands of soldiers' lives were lost as generals repeatedly attempted to charge through the killing zone called no man's land where these crossfires were set up.
The significance of crossfires is that they rendered useless what had been the most effective weapon of warfare since the Greek phalanx: massed infantry. Though World War II had more casualties overall, the soldiers died much more quickly in the battles of World War I as they went "over the top" in to the meat grinder known as no man's land.
Crossfires are limited in application, however, because they require a flat plain for greatest effect. This weakness is minor, however, because crossfires are best at destroying large blocks of infantry, which also require large, open planes.
The biggest weakness of overlapped crossfires is that they are stationary defensive positions. Three things changed between WWI and WWII that rendered the crossfire obsolete: the advance of armored vehicles (especially tanks), the advent of aerial bombardment, and the invention of the proximity fuse.
Tanks were invented in WWI specifically because they were immune to machine gun fire, and could thus cross no man's land to destroy the machine gun nests. Their armored hulls also provided cover for the infantry to advance around the tanks. The tanks in WWI were ponderously slow and prone to stalling, however, so they tipped the balance in the favor of the British, but not decisively. In WWII, the tanks improved greatly in speed and reliability, and could reach a machine gun nest at reduced risk since it spent less time exposed.
Airplanes were present in WWI, but they were used primarily for recon and the outcome of the battle in the air didn't have a lot of effect on the ground battle. The pilots often experimented with carrying things like hand grenades to drop on the enemy, but they were largely ineffective. In WWII airplanes could bomb enemy lines, rendering any large stationary target vulnerable to destruction. Fighters also strafed enemy lines with machine gun fire.
The proximity fuse allowed bombs and munitions to detonate when an object passed within a certain range (usually about 50 feet) rather than using an impact or timed fuse. Timed fuses are tricky because the range has to be pre-set correctly. Impact fuses are bad against flying targets because they have a very small targeting silhouette, and they're bad against ground targets because the projectile has time to embed in the ground before it explodes, deflecting the explosive power upward. Proximity fuses were developed by the U.S. Navy during WWII, and they proved instrumental in defending the fleets from aerial attack since a gunner using bullets with proximity fuses only had to get close to hitting the enemy to knock him from the sky. Proximity fuses were also instrumental in the battle for Britain because, after the gunners changed to proximity fuses, not a single German bomb made it past the guns. The fuse also permitted the heavy artillery to detonate above ground, permitting the explosive power to be fully utilized against targets on the ground. The trenches of WWI, for instance, wouldn't have been effective protection against a bombardment using proximity fuses.
Any of the above three technologies would have rendered the cross fire useless. Modern warfare has not returned to big blocks of infantry because the above inventions also kill massed infantry well, and with the perfection of shoulder launched rockets and precision bombing, stationary targets are too vulnerable to be as deadly as the crossfire was in WWI.