NATO nations in the path of recent Icelandic volcanic ash clouds, had to ground their combat aircraft. Even though the skies might seem clear, the ash is still up there. Ladar (laser radar) can detect the ash. Aircraft are not normally equipped with ladar, so they can fly into ash and not know it until the pilots notice the windscreens clouding up and the engines malfunctioning. Often the ash contamination is not discovered until the aircraft lands, and maintainers look inside the engines, or note some abrasions on the fuselage from ash.
As more jet aircraft took to the air in the last few decades, it was noted that volcanic ash was a major hazard for the fuselage and engines. Before that, it was rare for aircraft to encounter volcanic ash. They accepted that the ash was dangerous, but mainly from poor visibility. But as more and more commercial aircraft filled the skies, there were a lot more opportunities to fly through ash.
The damage could be substantial. The tiny particles thrown up by volcanoes scours the fuselage of fast moving aircraft, obscuring the windows (particularly those in the cockpit). But it's worse for the engines, which often stop operating. The engines can often be restarted, but once the aircraft lands, those engines have to be removed and rebuilt. One 747 took three months, and over $80 million to repair. Most of the expense was the damaged engines.
Despite the recent flight ban, NATO warplanes could still take off in an emergency, and using instructions from the ground, about where the largest concentrations of volcanic ash were, avoid damage. But for training flights, it's safer to keep the aircraft on the ground until the ash danger has passed.
The military is concerned about the new ash policies. Grounding aircraft over a large area is new. In the past, pilots were just told to stay away from the visible plume of ash blasting out of volcanoes. Subsequent research showed that dissipated (not visible at all) clouds of ash were also dangerous. But the military need to move their transports, and keep pilots in the air for training, to maintain their combat capabilities. The war in Afghanistan had a lot of military transports in the air over the affected area, and this was a problem. The air forces are now seeking better solutions to the ash problem.
Keeping commercial aircraft on the ground for a week revealed that the grounding order was based on imperfect knowledge of how much ash is a danger. The ash clouds eventually dissipate, and there is always some volcanic ash up there. This will spur more research into tracking, and measuring, ash concentrations in the air, and what concentrations are a threat to aircraft. Meanwhile, the airliners are flying again, as are many of the warplanes. However, some British Eurofighters were later found to have volcanic ash in their engines, indicating that the military have to be careful about exactly where they do their training flights.