NE555 - astable flashing alternative LED circuit
Your circuit redrawn is circuit 1 and there are two possible states circuit 2 and circuit 3.
Circuit 2 is the High state of the 555 timer. In this state the voltage across the top led is 0 (9V on anode and 9V on cathode) which means no current flows and the led is off. Meanwhile the bottom led is on because there is a positive voltage across its terminals (9V on anode and 0V on cathode.). This means that current flows from the 555 through the diode to the ground.
Circuit 3 is the Low state of the 555 timer. This state is the opposite of the previous. Now there is a voltage drop across the top diode and no drop across the bottom. This means that the top is on and the bottom is off. The current flows from the 9V source through the top led and into the 555.



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The internal circuitry of the 555 output pin is essentially this:



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