A schmitt trigger is a circuit that provides hysteresis: its threshold voltage depends on the current state. This is useful in preventing noisy sources from generating many spurious transitions in digital logic or when using a comparator.
R1 and R2 form a voltage divider, setting the comparator's threshold at VCC / 2. R3 sources or sinks a small current from the output into the positive terminal. When the output is high, this increases the threshold voltage slightly, and when the output is low it decreases it. This positive feedback provides a range of voltages for which the output will not change from the state it's currently in.