In an off-grid system there is no public electricity grid. Once solar power is used by the appliances, any excess power will be sent to the battery bank. An off-grid solar system is designed appropriately so that it will generate enough power throughout the year and have enough battery capacity to meet the users requirements during the day and night, through all the seasons. The high cost of batteries and inverter means off-grid systems are much more expensive than on-grid systems and so are usually only needed in more remote areas that are far from any electricity grid.
Once the battery bank is full it will stop receiving power from the solar system and power the load. When the solar system is not working (night time or cloudy days), your appliances will draw power from the batteries.