In a series circuit, there is only one possible path from one battery terminal, through the circuit, to the other battery terminal. All of the current that leaves one side of the battery travels exactly the same path to the other side of the battery. There's never any point in the circuit where the current has a choice of which way to go.
In a parallel circuit, there are different possible paths. On its way through the circuit, the current comes to a point where it has a choice of going this way or that way. What happens at that point is that the current splits up ... part of it goes this way, and the rest of it goes that way, and it all joins up together again somewhere else in the circuit.
