The opamp is used as a comparator in this simulation.
The real circuit uses TLC3702
http://www.ti.com/lit/ds/symlink/tlc3702m.pdf
The inverting input sets the treshold level for the comparator (1.84V - 37% of the 5V supply).
When the button is pushed, the 10uF capacitor is charged trough the 1K resistor (5RC=50ms). The voltage level on the non-inverting input of the comparator will rise above 1.84V, so the comparator pulls the output to 5V.
When the button is released, the 10uF capacitor is discharged trough the 6.2M resistor (RC=10uF*6.2M = 60sec)
After 1 RC time, the capacitor discharge to 37% of its voltage, below 1.84V, which is the treshold level set by the 620K and 360K resistors so the comparator pulls the output to ground.
