Carving is where the edges cut into the snow so well that the skis do not slide sideways, and travel straight along their length. Because the edges on modern carving skis are curved they cut into the snow in a slight arc, the skis then follow the edges and this takes you around in a turn.
To start carving the carve has to be initiated. This is best done as you are pointing straight down the slope, by rolling the knees over so that the ski edges dig into the snow and steer the skis across the slope. The skis need to be put on the edges enough that when they start turning the skis will cut into the snow and not slide. A common mistake made by people learning to carve is that they don’t roll the knees over enough, the skis really do need to be lent over to be sure the edges won’t slide. Once the edges are dug into the snow and the skis are traveling along their length, the skis will start turning and you will be able to push against them slightly and lean the body to the inside of the turn more. The faster you go while carving the more you will be able to lean, and the harder you can push on the skis.
When carving properly and leaning into the turn, the body’s weight should be transfered to middle of the outside ski. The body is also kept more upright than the legs to enable the edges to be dug into the snow as much as possible, this also makes it easier to switch between turns as the body does not need to be moved so far. The shoulders are brought flat to the direction of the skis, as the direction we are now traveling is straight forwards. Experienced skiers will also use the inside ski when carving to an extent, but this is only when the conditions enable them to really dig the edges on both skis into the snow.
Carving is not always possible, to carve you need to have the right equipment and the right conditions. With most equipment and conditions carving is possible to an extent, but to really carve properly you need the right set up. The snow should be soft enough that the edges can dig into it, but hard enough to hold the sideways forces that you create. In icy conditions is generally when people find it difficult to carve as the edges do not want to cut into the snow so easily. How sharp the edges of your skis are can make a big difference here, as the sharper they are the easier they will dig into the snow.
Watch the youtube video of this demonstration.