Series Circuits are characterized by a single pathway from the + to the - terminal of the battery. The bulbs are arranged in a consecutive fashion such that any charge that passes through the first bulb will also pass through the second and the third bulb. This explains why the current is the same in every bulb. As a charge passes through a bulb there will be a loss of electric pressure. We sometimes call it a voltage drop. Since charge passes through all three bulbs of a series circuit, there is a combined voltage drop resulting from each stepwise loss of voltage in each bulb. This combined drop in voltage is equivalent to the voltage of the battery. In effect, this total voltage drop is divided (unevenly between the bulbs in the series circuit. Adding a fourth bulb will thus decrease the voltage drop for all pre-existing bulbs since now the total battery voltage will have to be shared four-ways instead of three-ways.
Parallel circuits are quite different because the bulbs are all placed in an individual branch with each branch operating independent of the others. It is analogous to toll booths on a tollway. While each toll booth offers resistance to the flow of cars, placing each toll booth in its own lane (or branch) means that having more toll booth lanes will reduce the overall resistance and increase the flow of cars through the toll area. For circuits, it works similarly. Adding more bulbs will also add more branches (lanes) and decrease the overall resistance while increasing the flow rate or current.