Not too hot on the actual definitions etc, but here's a general description.Windshear most usually manifests as a change of wind velocity as altitude changes. The wind speed is usually stronger at altitude than close to the surface. The direction usually backs about 20 degrees at altitude compared with the surface, also, but this is extremely variable and depends on local effects (terrain) and the weather pattern/air stability on the day. The general descriptor of this is wind gradient, where the windpeed increases steadily and somewhat predictably with altitude. Shear is the more sudden relative.
Normally windshear is most significant on approach, where the aircraft is close to minimum speed, and as it descends enters an area of less headwind. Because the aircraft has inertia, this translates to a decrease in airspeed. If severe enough the aircraft may not be able to recover from the situation (Talking pretty darned severe, here, but it has caused accidents.)
The usual procedure where windshear on approach is reported or expected, is to carry a bit more airspeed. The usual procedure when severe windshear is encountered is to raise the nose and apply power, lots of power, as required. Naturally the nose shouldn't be raised so much the aircraft risks stalling, it's both intuitive and counter intuitive to do this. Intuitive (for the less experienced) because the aircraft is sinking below the normal profile; counterintuitive because it's unnatural to raise the nose if the airspeed is dropping. I believe it's been recommended as a windshear procedure, because it slows the descent rate initially, which is important, as the windshear is quite likely to get worse the faster altitude changes.
It affects all aircraft. Because light aircraft have less inertia, usually a lower descent rate on approach, and are less often landing on runways that are close to the minimum length than large airliners, it's usually not so critical. But definitely can be.
All that said, windshear can occur at any altitude, in any flight condition, given the right (wrong) met conditions. Often associated with jetstreams. Almost always occurs near/in thunderstorms.