Where does the oxygen released by plants during photosynthesis comes from?

During photosynthesis, light will hit pigment cells in photosystem II. The cells absorb this energy which is transferred from cell to cell until the P680 pair of chlorophyll molecules absorb it. An electron in this pair of molecules then becomes excited because of this extra energy, leaves the molecule and is transferred to the primary electron acceptor.

The movement of this electron leaves something like a 'hole' in the molecule that needs to be filled. While all this is going on, there's an enzyme that's splitting water molecules to give electrons, hydrogen and oxygen.
Remember that water's chemical formula is # H_2O#. The electrons will be used to fill the hole in P680, while the hydrogen will be used to make NADPH.

Oxygen is just a by-product of this splitting, and will be removed from the plant.

This diagram sums up everything. The black arrows show the energy movement from the pigments to the P680 molecule. An electron travels up to the primary acceptor and is replaced with incoming ones from # H_2O#. Notice that the oxygen is coming from water and it's being kicked out of the photosystem.