In a given series circuit of simple resistances, the current remains constant throughout the series string, while the voltage divides, or is dropped by each successive resistance.
In a given parallel circuit of simple resitances, the voltage to each parallel branch is the same, with the current s of each branch adding to yield the total circuit current.
Simply put, 5 15mA LED's in series will, if properly limited, be seen by the souce as a single 15mA load, whereas 5 15mA LED's in parallel, assuming each is properly limited to that current, will be seen by the source as a 75mA load. Hence, the parallel circuit will likely deplete the source (battery) more rapidly...