Kabardino-Balkaria is named after its native Kabardin and Balkar people. The Kabardin are a Circassian group related to the Adyghe, while the Balkar are essentially the same as the Bulgars, who migrated to present day Bulgaria. Both groups are Sunni Muslim.
The Kabardin speak Kabardian, a north-west Caucasian language of which "Cherkess" is a dialect; the Balkar speak Balkar, a Turkic language virtually identical to "Karachay." But fortunately for the visitor, all are fluent in Russian.
Mountain climbing is the biggest draw to Kabardino-Balkaria, and it's a serious sport here. The most popular climb is undoubtedly Mount Elbrus, as it is one of the "Seven Summits," and is actually a fairly easy climb in technical terms (Russian Grade: 2B). But bear in mind it's actually one of the world's deadliest climbs in terms of fatalities per climber—it's a long climb to the top and the mountain often has dangerous and unpredictable weather. Dykhtau and Koshtan-Tau are considerably more technically challenging climbs. Two of Georgia's highest peaks, Shkhara and Ushba, are also climbable from the Russian side. Although these climbs are technically illegal (since you cross the Russian-Georgian border), border enforcement is lax at 17,000 ft (5,000m). Take note, though, that the Shkhara climb is a lot easier and safer on the southern face.
Because dealing with Russian officialdom is hellish bordering on impossible, it's best to embark on a mountaineering expedition via guided tour (the tour agencies pick you up from Mineralnye Vody or Nalchik right at the airport and act as your intermediary with all Russian officials. Russia-based tour agencies are way cheaper than Western ones:
While not as involved in the general conflict across the North Caucasus, Kabardino-Balkaria, especially Nalchik, has been attacked repeatedly by rebel and terrorist forces. Expect a very tight security situation, realize that this is an unstable and dangerous part of the world, and make your travel plans accordingly.