The white stuff is sulfuric acid, don't get it on your skin or clothes,
Best thing is to neutralize it with Baking soda and water while cleaning it off, make sure you rinse it off all of the metal below the battery.
Just sprinkle on the baking soda and add some water, do NOT spray water at it, sulfuric acid will get everywhere, sprinkle and rinse.
Then remove battery cables and clean those and the posts, wire brush is good, also you can buy a cheap tool for cleaning battery terminals and cables.
Batteries vent hydrogen gas, this gas reacts with the copper and lead in the battery cables/terminals and creates the sulfuric acid coating.
This can get inside the battery cables rubber coating if left uncleaned long enough, so if it looks like the copper is corroded cut back the insulation and clean it, if its bad, replace that cable.
The hydrogen gas venting increases with the charging of the battery, so when you see this type of build up your charging system might be a bit out of wack.
A battery(with clean terminals, lol) should have 12.4-12.8volts(key off).
After starting the engine battery voltage should go up to 14.2-14.8volts(battery is being re-charged from starting engine)
Then after a few minutes of idling the voltage should drop down to 13.5-13.8volts, that's the voltage regulator working as it should.
1 volt above battery voltage will maintain battery's charge, more than that will cause constant hydrogen venting.
If voltage stays above 13.9volts after a few minutes of idling then battery is being over charged, so venting hydrogen, the cause of this could be voltage regulator or wiring(voltage regulator "thinks" battery voltage is low).
If your battery voltage was below 12.4 volts(key off) then battery could be going bad, a shorted cell, this would also cause regulator to continue charging battery