One of the main reasons for using opamps as active devices in circuits is that their internal gain is so high, that even if we reduce it to a tiny fraction, it will still be enough for practical purposes. This particular configuration depends on the very high gain of the opamp to swing the output to one of the extremes; the sign of which tells us which input is more positive than the other.
By connecting the non inverting input to a voltage source, we are setting the reference point of the comparator. Remember that since there's no feedback, and because internally the opamp is just a very high gain difference amplifier, the output will be the non inverting input voltage minus the inverting input voltage, multiplied by the internal gain (in the 100k's).
This means that a difference of just millivolts will drive the output into saturation; if the difference is positive it will swing to full positive, limited by the supply. If the difference is negative, it will swing to full negative, again limited only by the supply.
On most amplifier circuits it is not advisable to drive the opamp into saturation because it clips the signal from going any further on both ends, but in this case we are not so much interested in the signal itself but on the relationship between the signal and a reference, so this circuit serves its purpose.
