True. Windshear can happen anywhere; it's just a change in direction or velocity, and windshear can be vertical or horizontal, close to the ground, or at altitude in cruise flight. Vertical shear is what's often felt as turbulence in various forms, horizontal shears are more of a cockpit indication, roughly speaking.
The microburst that GalaxyFlyer mentioned is something that comes from thunderstorms, or "convective activity." That's the lifting and falling of air based on heating from the earth's surface, sometimes thanks to terrain or tall buildings, sometimes due to surface heating like factories or forest fires and occurs in an unstable airmass. Air is heated, becomes less dense, rises, cools, and falls. When it does, the changing air properties change the ability to hold moisture and energy; hot air can hold more moisture, cool air not so much. When moisture is released, latent heat energy is released. When moisture evaporates, it causes cooling, and descending air falls faster the more it cools. Rain falling out of descending air causes the column of air to fall faster, and it can descend at very high rates of 6,000 feet per minute or more. When that column is encountered by an aircraft, it's a downdraft. When the column reaches the ground, it spreads out, just like pouring water on the ground, and as it spreads out, it forms a gust front. These are referred to as microbursts; downdrafts that reach the ground and can rob so much performance from an aircraft that it may not be able to overcome the loss.
When you hear about windshear warnings and predictive windshear and things like that, mostly we're taking about thunderstorms and big hazards like microbursts. If a airspeed increase occurs flying into a microburst, then it's what we call an increasing-performance windshear encounter. The airspeed jumps up, the aircraft has more lift, and it will try to climb above the glideslope. The nose must be lowered, power reduced, to stay on the glidepath to the runway. The aircraft will slow down with a headwind; it's physical energy decreases as it slows; it it has less inertia. Passing under the microburst, the wind is from above; a strong downdraft. At this point any extra benefit of the wind increase at the gust front is gone. The aircraft has less kinetic energy; it's slower, now has less airspeed, less power, and it's being driven downhill; this is all happening in a very short period of time. We're now into the downdraft phase of the microburst, and full power may not be enough to overcome.
The goal at this point is to prevent ground contact. The best known mishap regarding a microburst was Delta 191 at Dallas, Ft. Worth (one I remember very well). It was a victim of just such an event, and the reason that training systems all incorporate windshear training today. At t his point, the crew may have gone to maximum power to overcome the downdraft, the aircraft is slow, pitched up and slowing, and doing everything possible to prevent ground contact. The procedure is to fly the aircraft right to the stick shaker (stall warning) if needed; prevent the aircraft from touching the ground at all costs. There's been a bit of modification to the procedure over the last few years, but the main points remain: stay alive, stay airborne.
As the aircraft transitions to a tailwind, there's a further performance loss. Already slow, already low on energy, now the aircraft has a further airspeed loss, a tailwind, and the struggle gets worse. it will begin to move faster over the ground, but it's going to have a loss of airspeed at a time when it may already be on the edge of a stall, with the stall warning systems active. The aircraft will already be at maximum power; there's no more reserve to go get. As Scottie on Star trek would say, "I'm givin it all I can, captain; I can't give her no more."
If done correctly, and in time, the aircraft flies out of the microburst and gives adequate warning that others don't have to go through the same thing.
What we do is mostly prevent ever being there in the first place. We avoid landing when there are thunderstorms near the airport. We have predictive windshear capability on many transport category aircraft, that works as part of the radar to map airflow by noting the velocity and direction and change in both of moisture on radar returns, to predict where windshear might be. Many airports have LLWAS, or a low level windshear alerting system, which is a doppler radar system that works in a similar manner to the onboard predictive windshear system in the aircraft, but on a broader scale ,with more capability. Air Traffic Control broadcasts windshear warnings, etc.
What GalaxyFlyer noted was that the windshear encounter I've just described is typical of thunderstorms, which are seldom found in the wintertime (they can be). Gusty conditions are common in the winter, and don't have all the components of the microburst; typically they're simply wind changes that can produce airspeed loss or gain, and make the flying a bit more demanding. Increases in airspeed may delay touching down, or may result in a touchdown a bit faster than one planned (eg, airspeed loss), resulting in some of the entertaining videos one sees on youtube, in really gusty conditions. The approach and landing is kept as stable as possible, with small corrections for changing wind and conditions.
The 15 knot wind increase warning is just a heads up of what to expect, or at least, what others encountered.
I should add that conditions don't have to be turbulent and particularly gusty to have that speed change. In the wintertime, in cold air, a point where there's a marked temperature change will typically have a windspeed change, too. There are different wind properties in the two parcels of air. It's not uncommon to have an inversion, in which the air gets colder close to the ground. The cold air is trapped by warm air above. One might have a 15 knot tailwind on approach, but the air beneath the inversion is still, calm; when the airplane passes from the tailwind to calm air, it will be seen as a 15 knot speed increase. Why? The tailwind is pushing the airplane an extra 15 knots over the ground, and when it hits the still air, that speed will register as extra airspeed (think of it as punching a pillow, when your fist encounters the increasing resistance of the air or pillow, if that makes sense). The aircraft hasn't actually encountered a headwind, but the reaction will be the same. There are a lot of variations on a theme.
Typically there would be a turbulent layer where the tailwind meets the calm air; one air parcel moving over another causes friction or turbulence at the boundary, and once into the calm air, it maybe perfectly still.
When flying an approach, we have indications in the cockpit showing the wind vector. We can look at the wind vector of a tailwind, for example, and look at the reported surface wind at the runway, and determine what kind of change we might get. In most cases, the wind decreases as we get closer to the ground (friction from the earth's surface, and interference from obstacles, terrain, etc, slow the wind velocity close to the ground), so much of the time the wind actually gets to be less, though it often gets a bit more turbulent as the air is spilling around trees, buildings, hangars, etc, assuming there's any significant wind to begin with.
As you can guess, a headwind means the aircraft touches down with a slower groundspeed, consequently a shorter landing roll, and a tailwind has the opposite effect. A crosswind can go either way, depending on how much the crew is doing to counter the crosswind, and if it delays touchdown. In most cases, it's a simple transition from straightening the nose to point down the runway while lowering a wing into the wind, ideally happening at the same moment as touchdown. After touchdown, spoilers are deployed to kill lift on the wing and put weight on the wheels, to prevent gusts from lifting a wing, and to ensure that the brakes can be as effective as possible.