An inverter is the crucial accessory you need to run mains-powered devices from battery-supplied DC.
Converting 12V to 240V is not a big deal: that’s simply a matter of a suitable transformer.
Rapidly switching the polarity, in a similar way to the AC (alternating current) supplied by mains power from the electricity grid, is a more complex proposition.
Modified sine wave
Simply reversing the polarity of a DC supply at a rapid rate will result in a square wave, which does not provide enough voltage variation over time to support the effective functioning of many AC-powered devices.
In reality, 'modified sine wave' is a euphemism for 'interrupted square wave'. The voltage still jumps in sharp, stepped fluctuations, but a flat period of zero voltage is introduced between the positive and negative pulses. The current supplied by a modified sine wave inverter approximates mains AC enough to work satisfactorily for things like laptop power supplies, which usually rectify the current back to DC in the first place.
Pure sine wave
For more sensitive appliances, for example, those that use an AC induction motor, a PSW inverter is a better option. This normally uses a MOSFET driver or a combination of PWM (pulse width modulation) and capacitor filtering to minimise the harmonic distortion (in other words, the 'roughness' or 'choppiness') of the waveform.
This PSW inverter can deliver an impressive 1500W and includes a built-in 30A PWM (pulse width modulation) solar charge controller. It will support power-hungry appliances such as power tools, but you'll need to keep an eye on your battery: drawing that kind of current will quickly deplete it.
Click here to learn more about inverters.