Fjellski - literally mountain skis - are wider, longer and slightly heavier than standard langrenn skis, built for off-track travel through the open Norwegian mountain country in winter. The classic fjellski is approximately 200-210 cm long, 50-65 mm wide underfoot, and uses a free-heel binding (typically the Norwegian-developed NNN-BC or the older 75mm three-pin) with a stiff leather or modern plastic boot. The combination is faster on long flat distances than alpine ski-touring, lighter than snowshoes, and capable of handling moderate descents in non-technical mountain terrain.
The fjellski tradition is the original Norwegian backcountry tradition. Long before alpine ski-touring became fashionable, generations of Norwegian mountain travelers - the DNT hut network was originally built around it, the polar explorer Fridtjof Nansen used it for his 1888 Greenland traverse, Roald Amundsen used it on the way to the South Pole - moved through the inland Norwegian winter on something close to the modern fjellski. The standard hut-to-hut Easter tradition (påsketur) when most of the country takes a week off and travels through the high mountain country on skis is essentially a fjellski tradition.
What separates fjellski from the more familiar alpine ski-touring is the equipment philosophy and the terrain. Fjellski are designed for the broad open vidder - Hardangervidda, Finnmarksvidda, the Jotunheim plateau - with long flat or gently rolling distances and modest descents. Alpine ski-touring (topptur) uses much wider, shorter skis with releasable bindings and AT boots, and is built for steeper terrain, technical descents and the maritime peaks of Sunnmøre and Lyngen. Both are valid; they are different sports.
For the international visitor, fjellski is the right format for most of the long-distance Norwegian cross-country trips - Hardangervidda crossings, the Jotunheim ski route, the Trolløypa, the Peer Gynt. Equipment can be rented at most destinations and the technique (waxed kick-zone for grip on the climb, glide on the descent) is straightforward to learn. The longer ski plus stable boot makes an off-track route through deeper snow much easier than narrow track skis. See A winter week at Hindsæter.