Suppose R1 and R2 are the resistances connenected in series. The R1 and R2 are connected in sries across a voltage V. The resitance R2 is not connected direcly to the source it is connected to the resistance R1. So it recieves its voltage from R1 after a drop. Whereas in a parallel circuit the both R1 and R2 are connected to across the same voltage directly and R2 . In as series connected resistors (or components) the same current flows through all the resistors, but voltage drops from resistor to resitor and the sum of the voltage across each resistor(or component) is the total voltage . Whereas, in a parallel connected resistors, the voltage across each resistor (or component) is same whereas the sum of the current through the components is the total current of the system
Potential difference in any part of a circuit is equal to the difference in the potentials of the start and end point of the the part of circuit being considered. Parallel circuits are by definition circuits that have common start and end points. The starting point of all the parallel circuits being the same, the potential at their start point is also same. Similarly the potential of end point of all the parallel circuit is also same. The potential of start and end point of all parallel circuits being same, their potential difference is also same.