What is the purpose of this circuit?

The opamp in the circuit is actually a voltage comparator, it's designed to output only 2 voltage levels - high and low. The positive feedback makes it Schmitt trigger -circuit (=a comparator with hysteresis) to make the comparator a little faster and to increase noise immunity.

The transistor is pulse amplifier. The capacitor makes it have low pass filter action to reduce noise. The amp is clearly designed for pulses, the linear range is narrow and difficult to predict. The circuit has pull-up in the input, so it can well be driven only by a switch which connects the input to GND.

I guess the circuit is intended to clean a signal which either is a connection to ground with a switch or transistor. The input can as well be a voltage which has 2 intended states: 0V and 5V.

RxD refers serial data communication. The input stage suggests a low bit rate.

Q4, R40 and R44 form a pullup and buffer that can tolerate quite high voltages for a logic low (up to about 3.6V depending on temperature) from a relatively weak sink of perhaps < 1mA.

C22 and R46 form a noise filter (-3dB at about 3.4kHz).

U7 and surrounding circuitry is a comparator with significant hysteresis that also limits the output high voltage to about 3V (the divider of R7 and R8 do this as the comparator is an open collector device).

R45, R43 and R47 set the comparator threshold with hysteresis; the thresholds are about 1.7V (output low, input high) and 3V (output high, input low).

So this circuit is buffering the source, doing noise reduction and level shifting the output to be suitable for the RXD destination from a weak (possibly quite distant) and noisy source.