With a backup battery, the excess energy that your solar panels create (but your home does not use), will be stored in this battery. Then, when the sun is not shining, this battery will provide your power during the night, system blackouts or inclement weather. With a hybrid solar system, if you were to use up all the power in your battery, you have the ability to draw power from the electrical grid.
A hybrid solar system works by sending solar power to your inverter, which then sends energy to power your home. Extra energy that is not used to power your home goes to your home battery for storage. This battery can provide power to your home when your solar panels are not producing energy. After all of those steps, if there is still leftover energy, that energy is sent to the grid.