How does this circuit work to fade an LED in and out?
Q1 is an emitter follower. The voltage on the emitter is the capacitor voltage minus 0.7V or so. 

If the LED Vf is 2V then the current through the LED is about (Vc1-2.7)/470. So at 3V on the capacitor, the LED is almost off.

The base current is about 12-25uA (depending on transistor beta) when the capacitor is at 6V (peak) so it will lengthen the cycle a bit, depending on the type of 555. A bipolar type will output about 7.8V with light current, so the current through R1 will be only about 55uA, so it might fail with a BC547A.