Battery storage allows you to store electricity generated by your solar panels for use in the evening.
A typical home with solar sends any electricity that is not used by the home out to the grid. In return, the household gets paid a feed-in tariff from the electricity retailer.
Once you add a battery system to the solar panels, instead of sending out the excess electricity to the grid, that energy is stored by the battery.
You can then use this power when your solar panels are not generating electricity, allowing you to buy much less electricity overall from the grid. The below diagram provides an overview of the process.