A battery rated at 10 amp hours can supply 1 amp for 10 hours, or 10 amps for 1 hour, or 2 amps for 5 hours, etc. To determine approximately how long you can run your pond equipment on the battery, divide the amp hour rating of the battery by the amps required by the inverter - the result is your run time in hours. If you need more battery capacity, you can put multiple batteries in parallel. If you put batteries in parallel, don't mix and match - only use new and identical batteries. The inverter is used to convert the 12VDC from the battery into 120VAC for use by your pond equipment during power failures.
Inverters are available with outputs of just a few watts to thousands of watts.
To get the longest backup duration, you should put the minimum amount of equipment on the battery backup system as possible. You should also select an inverter that is able to meet the demand of this equipment, but which is not excessively over sized. An oversized inverter will not be as efficient. Make sure your pumps work ok with your inverter. Most pumps will also have a much larger startup current than running current.