What process does this represent? It looks like separating water into its component gases but not sure.

This is just the chemical reaction of water. Some call it chemical bonding.

H20(water) is 2 Hydrogen and 1 Oxygen.

You need 2 Hydrogen for every 1 Oxygen.

2H2 gives you 4 molecules of Hydrogen
O2 gives you 2 molecules of Oxygen


2H2(4 hydrogen) + 02(2 oxygen)= 2H20

Kendor you are correct. The direction of the arrow indicates the reactants going toward products. In this case you are dissociating the water into the component gases.
This direction is not spontaneous. Most often I've seen this reaction named in the process of electroysis of water. It requires energy(work) to make it happen. (The formation of water from the elements releases energy in the form of heat).

Clarebear is close.. To balance the equation for normal form of 1 oxygen molecule (2 atoms)
and 2 hydrogen molecules (4 atoms) we need to break apart 2 water molecules.