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.