Carving skis are called parabolic skis: they are shaped, in other words, they are wide at the ends and with a narrow width in the middle. They were first developed in the 90s and feature important advantages compared with traditional skis: more control, stability and easier turns.
Parabolic skis have revolutionized downhill run, and the carving technique, consisting in turning perfectly, without sliding or skidding, has become more and more popular among downhill runner, and nowadays it is the most widespread. The reason is easy to understand: with shaped skis, all skiers with a fairly good technique can make a carved turn, without skidding and without losing speed, leaving clean and harmonious traces on the snow: this is what all alpine skiers dream, and in the past only great champions were able to do it.
Now skiers can have a higher control on skis, and all descents are easier, faster and make more fun, even for those who cannot ski perfectly yet. Furthermore, carving can be learnt more easily and beginners can make big progresses in a short time, whereas "experts" can further improve their performance.
Fun carving is a further evolution of carving: this technique uses short and very shaped skies, with no ski poles. Unlike carving, fun carving is not a sport for everybody: in fact, you need an excellent technique and a very good athletic preparation.