Why does current split between branches of a parallel circuit, but voltage remains the same for each branch?

Current is the rate of flow of charge in a circuit; you can imagine the flow of electrons as water flowing through a pipe. If the pipe splits into two, some of the flow will go through one pipe and some through the other. The flow in either pipe is less than the flow in the original pipe. Similarly, if the electrons travelling round a circuit come to a branch in the circuit, then some electrons will go through one wire and some through the other. Therefore, the rate of flow of charge is reduced in each branch compared to the original wire (electrons have a fixed charge and will be travelling at the same average speed). So current splits between branches in a parllel circuit.

Voltage is a measure of energy (in Joules) per unit charge (in Coulombs). As each electron has the same charge, each electron is carrying the same amount of energy, so the voltage across each branch of the parallel circuit will be the same because the voltage doesn't epend on the number of electrons in each branch. Returning to the water flow analogy, if a flow of water split into two before going over a waterfall. the water in both streams would still fall the same distance before meeting again at the bottom.