Thanks to the eloquent writers over at Allmusic.com:
In the late 1950s, Stockhausen became increasingly influenced by the aleatoric music of American composers like Morton Feldman and John Cage, as well as by American jazz. These influences are evident in Kontakte, though it is a work that clearly belongs to the European avant-garde tradition. It also presages developments in Stockhausen's own style, including elements -- such the addition of instrumentalists to an existing tape composition -- central to his later works.
The title refers to the moments of "contact" between the electronic sounds on the tape and the live performers. The tape consists of percussion sounds altered by different electronic means, including a ring modulator, a reverberator, and an impulse generator. The instrumental parts intertwine with the taped sounds, creating a wildly diverse array of textures and timbres over the course of six sections, or "moments." The moments are determined by events on tape, but the instrumentalists also participate in the transition from one moment to the next by changing character. Each moment contains six subdivisions of intensity, from "just noticable" to "violent," that refer to variations in acoustical phenomena including volume, speed, and register. The pianist and percussionists must respond and interact carefully with the tape, ensuring a proper balance of dynamics and intensity.