T1 is a simple common emitter inverter.
CNTRL_L0 is the input, and the node between
Q2 is the output. If the input is high, the output is low. If the input is low, the output is high.
Q2 is just another inverter, but it uses a MOSFET instead of a BJT, and because this is a P-channel device, everything is upside-down. In this circuit, as is conventional, the P-channel MOSFET is drawn with the source at the top, and the drain at the bottom. It's on when the gate is at a lower voltage than the source. So in this circuit, connecting the gate to
Q2 on. Connecting the gate to
IRF9Z34 is a power MOSFET device, so we can infer that it's intended to pass large currents. I don't see where the schematic shows how the LEDs are connected, but it's a safe bet that these large currents are due to the potentially many LEDs connected to this node. A P-channel device is needed because each LED has a separate switch already on the low side, so this circuit must switch the high side. Effectively:
simulate this circuit – Schematic created using CircuitLab
C8 is simply a decoupling capacitor, to reduce power supply impedance and filter switching noise generated by this circuit.
The net effect of these two inverters is no inversion. When
CNTRL_L0 is high,
T1 is saturated, pulling the gate of
GND, turning it on. When
Q2 is on,
ANODE_LEVEL_0 is effectively connected to
+5V, providing voltage to illuminate the LEDs (if their individual low-side transistors,
Q3 are also on).
CNTRL_L0 is low,
T1 is off. The gate of
Q2 is pulled high by
R3, switching it off.
ANODE_LEVEL_0 is then connected to
R4. In this condition, both ends of the LEDs will be connected to
GND, so can be no voltage across them, so they will not be illuminated.
It would have been possible to connect
CNTRL_L0 directly to the gate of Q2. This would invert the logic, but the controller programming could take that into account. However, power MOSFETs have significant gate capacitance, at it takes significant current to switch them. It's likely that the shift registers selected did not have enough current drive capability to switch the power MOSFETs sufficiently fast.