Direct current (DC) arc plasma torches are widely used in various industrial applications. Studying processes in their anode area helps to extend their lifetime, and stabilize the plasma flow for plasma applications. This paper reports detailed observations of the fast movement (above 100 m/s) of the anode arc attachment in a hybrid water-argon DC arc plasma torch with an external anode. We measured a mean electrical conductivity of a plasma volume above the anode and found a relation between the attachment movement and the anode erosion. Further, we measured average attachment speed, the average period of the restrike process and the average distances travelled by the attachment under different experimental conditions such as different values of the arc electric current, argon flow rate and different anode configurations. For our measurements, we used a high-speed camera and a high-voltage probe. Our results are in agreement with a model of plasma generated by a hybrid plasma torch and with spectroscopy measurements. The results describe the movement of the anode arc attachment in detail and provide experimental data on average plasma electrical conductivity in hot anode areas. Both the measurements of the mean electrical conductivity and the procedure for quantitative comparisons of anode erosion can be used also in water plasma torches and theoretically also in gas plasma torches.