Yes if you want to install a PV system with batteries, you have two options.
The first is to install a battery backup system to your PV system. Some inverters incorporate a battery backup system and others use a backup system that connects to your inverter before it is fed back to the grid. These allow you to store some of the energy you generate in batteries so that in the event of a powercut you can supply certain household items with electricity such as your lights and fridge. There are continuous improvements being made to these systems so that with some equipment you can now also run certain appliances at night to make the most out of the energy you generate.
The second option is to install a fully off-grid system which has a large battery capacity and can store enough energy to power the whole home. These systems are designed to give you complete independence from the grid and in remote areas with poor or no connection to the national grid can be an excellent choice. The PV system stores energy during the bay as well as powering the home, and then the property switches to battery power at night.
Batteries add significant cost to any PV system, and so are normally only offered on specific request.