A BESS (battery energy storage system) used for load-levelling on the electricity supply grid is generally a large number of batteries in a facility that are connected to one of the main feeders of the high-voltage electrical supply grid through DC/AC conversion equipment.  It has the purpose of matching the supply to the demand, drawing energy from the grid when the supply exceeds the demand, and supplying additional power when the supply cannot meet the demand.  This allows technologies such as solar and wind power to be used without needing to have as much excess power generation capacity as would be needed without a BESS, due to the mismatches between when in the day maximum power can be generated and when the maximum power is consumed.  Historically, gas turbines were often used to provide additional power in times of excess demand

The batteries themselves are the size of a shipping container.  The proposal for Marchurst is for 248+ shipping container sized batteries.

If you would like to understand how BESS works in more detail, there is a good article here.