In parallel circuits the currents flowing around the circuit "splits" as it meets the junction with another branch of the circuit, so some of the current will travel off along one branch with the remainder of the current travelling along the continuation of the parallel circuit until it meets another junction whereupon it will split off a little bit more. A diagram of such a circuit may help at this point you to visualise what's going on.



In the circuit above (assuming of course that the switch is closed, I have just left it shown open as a convenience in this case) a potential difference of 12 V passes around the circuit producing an overall current of 1.8 A as shown.


Three identical filament lamps on three identical branches of the parallel circuit each draw 0.6 A from the total. Therefore, you should be able to see that the total current on the circuit is equal to the sum of the individual currents on the individual branches.