Why current remains same in series?

An electrical current is a flow of charge through a circuit. In a series circuit there is only one path for the charge to flow through; therefore, (in a DC circuit) the same charge must pass through every point in the circuit.

It's not quite the same as flow in a water pipe. In a water pipe if you increase the flow of water at the intake end it will take some time for that increased flow to makes it way to the output of the water pipe. In an electrical conductor, changes are effectively instantaneous. As soon as you change the input flow the output flow changes too, and that implies that the flow at all points in between the input and the output have to be the same.

Once you see that please remember that this is the 'ideal'. The situation becomes considerably more complicated once you started learning about other circuit elements.