The battery backup described here is relatively inexpensive and you can use whatever size battery you need to meet your capacity requirements. The switching relays control the flow of power. While power is being supplied by the electric company grid, the relay coils are energized, the pond equipment is being powered by the grid, and the battery is being charged. When the power fails, the relays switch and the battery is now connected to the inverter, and the pond equipment is powered from the inverter. DPDT indicates that the relay is double pole, double throw.
Double pole means that there are two switches.
Relay R1 controls where 120VAC is taken from to supply power to the pond equipment. When grid power is on, the relay is on, C1 and C2 are connected to NO1 and NO2, and the pond equipment is powered by the grid. When the grid fails, C1 and C2 are connected to NC1 and NC2, and the pond equipment gets power from the inverter. Relay R2 controls how the battery is connected. When the grid is on, C1 and C2 connect to NO1 and NO2, and the battery gets charged.