Why is this line connected to the microcontroller input in this schematic?
They are to avoid excessive inductive voltage pulses when the PNP transistor is stops conducting to allow the relay to turn off.

When Q4 and Q2 or Q5 are turned on the PNP transistor will conduct and apply voltage to the relay coil.

When the PNP transistor turns off the current in the relay coil will reduce, but its inductance will cause a voltage backswing that in this case will make the collector of the transistor fall down to zero and attempt to go negative. D1 and D4 will start conducting then and prevent a damaging voltage across the transistor.

If the relay is turned off by Q2 or Q5 ceasing to conduct a similar action will occur only in this case the drain of Q2/Q5 will go positive; D2 and D3 prevent the voltage going above the 24V rail.