Array of atmospheric pressure surface discharges confined by a two-dimensional hexagon electrode mesh is studied for its discharge modes and temporal evolution so as to a theoretical underpinning to their growing applications in medicine, aerodynamic control, and environmental remediation. Helium plasma surface-confined by one hexagon-shaped rim electrode is shown to evolve from a Townsend mode to a normal and abnormal glow mode, and its evolution develops from the rim electrodes as six individual microdischarges merging in the middle of the hexagon mesh element. Within one hexagon element, microdischarges remain largely static with the mesh electrode being the instantaneous cathode, but move towards the hexagon center when the electrode is the instantaneous anode. On the entire array electrode surface, plasma ignition is found to beat an unspecific hexagon element and then spreads to ignite surrounding hexagon elements. The spreading of microdischarges is in the form of an expanding circle at a speed of about 3 × 104 m/s, and their quenching starts in the location of the initial plasma ignition. Plasma modes influence how input electrical power is used to generate and accelerate electrons and as such the reaction chemistry, whereas plasma dynamics are central to understand and control plasma instabilities. The present study provides an important aspect of plasma physics of the atmospheric surface-confined discharge array and a theoretical underpinning to its future technological innovation.