The op-amps are functioning as signal frequency detectors and activate LED's as indicators when certain input signal frequencies are input that match the band-pass frequency of the op-amp circuits.
So, the op-amps are used to make a frequency detecting circuit, with a different frequency being detected by each op-amp.
A common use of a circuit like this would be to detect certain frequencies to activate some control circuits.
For instance, a dual-tone frequency signal generated by a telephone keypad or some other device output could be sent over a single wire to create a multi-frequency signal used to control one or more remote circuits by detecting pairs of frequencies.
A single frequency input to the op-amps could be used to detect just one frequency of interest, so it would be possible to select the LED of interest to be lit, or music sounds could be input to activate the LEDs as a light show that responds to the different frequencies of various instruments.