BLDC Commutation and output states of half bridges
I presume GLx, GHx and SHx probably mean something like "Gate Lowside 'x'", "Gate Highside 'x'" and "Source Highside 'x'" x just denotes transistor pairs/half-bridges 1,2,3.

The L or H state in the columns below GLx and HLx refer to the transistor being switched on or off (L=low/OFF,H=high/ON) or rather it is the state on the gate of the transistor, and in the SHx column it refers to the output of this half-bridge being high or low. the reason you see "high-Z" in the SHx column is because the output can be "high impedance", z=impedance, meaning that no current can flow into or out of the half-bridge, in contrast to the L or H states where the output is pulled fully to GND (L) or Vcc/supply (H). This happens when both the high-side and the low-side transistor of the half-bridge are turned OFF