The effective development of modern welding technologies and the improvement of equipment and materials inevitably require deep theoretical knowledge about the physical phenomena occurring in the electric arc column and in the near-electrode region. However, there is still no convincing theoretical description of an arc discharge. This article demonstrates, through the generalization of known experimental facts and studies using a high-speed camera, that the conductive channel of an electric arc has a discrete structure, consisting of a set of thin channels through which the main discharge current passes. The cathode spot of an arc discharge is a highly heated and brightly glowing area on the cathode’s surface. Electron emission occurs from this region, which supports the discharge as well as the removal of the cathode material. We propose a new technique to study the reverse side of the cathode spot, revealing a structure consisting of individual cells or fragments of the cathode spot. For the first time, we present the anode spots captured by a high-speed camera. We carry out an analysis of the spots’ structure. We determine the parameters affecting the mobility of cathode and anode spots. We propose a hypothesis based on the obtained experimental facts about the heterogeneous structure of cathode and anode spots in an arc discharge and the existence of current filaments that affect the mobility of spots during arc combustion.