This circuit operates a LED in pulsing mode, i.e. the LED goes from off state, lights up gradually, then dims gradually, etc.
This operation mode is obtained by a triangular wave generator formed by two op-amps contained in a very cheap 8 pin DIL case IC. Q1 ensures current buffering, in order to obtain a better load drive.
R4 & C1 are the timing components: using the values shown in the parts list, the total period is about 4 seconds.