Drum shields allow a sound technician to contain the sound of the drums within the area outlined by the shield. They allow the technician to not only capture a cleaner drum sound by shielding the drum microphones from outside interference, but also keep the drums from being picked up by other microphones. This can be most useful when shielding the overpowering sound of the cymbals from other microphones on the stage or in the studio.
When a drummer plays a large hall, the drum sound can sometimes carry to the point where the drummer can no longer hear any definition in his playing. This is why some drummers need to hear their snare and bass drums from their stage monitors. A drum shield reflects all of the sound back to the drummer, eliminating the need for the drums to be in the monitors and allowing the monitor technician to get a cleaner mix on the other instruments for the drummer.
As was mentioned previously, drum shields reflect sound rather than absorbing it. Because of this, it can get extremely loud for a drummer behind a drum shield. The excessive volume can also make it difficult to get a proper microphone mix. One of the remedies is to put a wall of soft material behind the drummer to absorb the sound as it reflects off the shield. But in the case of live performance, that is not always possible.
In a live setting, a drum shield can be a problem for the rest of the band. The band is used to following the drummer's tempo and getting some song cues from the drums as well. A drum shield can reduce the ability of the band to hear the drummer, including those instances where the drummer counts off the song's beginning with his sticks. Unless the entire drum kit is heard from everyone's monitors, the drums can be difficult to hear. This can create problems when doing monitor mixes as well, because the high end of the cymbals can interfere with the sounds of vocals and other instruments.