What is electrolysis:
The process in which we use an electric current to cause chemical changes is called electrolysis.

How Does it Work?

The chemical equation for electrolysis is:

energy (electricity) + 2 H2O -> O2 + 2 H2 .

At the cathode (the negative electrode), there is a negative charge created by the battery. This means that there is an electrical pressure to push electrons into the water at this end. At the anode (the positive electrode), there is a positive charge, so that electrode would like to absorb electrons. But the water isn't a very good conductor. Instead, in order for there to be a flow of charge all the way around the circuit, water molecules near the cathode are split up into a positively charged hydrogen ion, which is symbolized as H+ in the diagram above (this is just the hydrogen atom without its electron, i.e. the nucleus of the hydrogen atom, which is just a single proton), and a negatively charged "hydroxide" ion, symbolized OH-:

H2O -> H+ + OH- .

You might have expected that H2O would break up into an H and an OH (the same atoms but with neutral charges) instead, but this doesn't happen because the oxygen atom more strongly attracts the electron from the H - it steals it (we say the oxygen atom is more "electronegative" than hydrogen). This theft allows the resulting hydroxide ion to have a completely filled outer shell, making it more stable.

But the H+, which is just a naked proton, is now free to pick up an electron (symbolized e-) from the cathode, which is trying hard to donate electrons, and become a regular, neutral hydrogen atom:

H+ + e- -> H

This hydrogen atom meets another hydrogen atom and from a hydrogen gas molecule:

H + H -> H2,

and this molecule bubbles to the surface, and wa-la! We have hydrogen gas!

Meanwhile, the positive anode has caused the negatively charged hydroxide ion (OH-) to travel across the container to the anode. When it gets to the anode, the anode removes the extra electron that the hydroxide stole from the hydrogen atom earlier, and the hydroxide ion then recombines with three other hydroxide molecules to form 1 molecule of oxygen and 2 molecules of water:

4 OH- _> O2 + 2 H2O + 4e-

The oxygen molecule is very stable, and bubbles to the surface.

In this way, a closed circuit is created, involving negatively charged particles - electrons in the wire, hydroxide ions in the water. The energy delivered by the battery is stored by the production of hydrogen.