What does 105ah@20hr mean for a battery?

The larger the better if it physically fits.

In deep cycle marine batteries the AGM type is best and a series 31 is about the largest size and current rating you will find at most stores.

The 8D size is the largest of all but are hard to find and very expensive.

My camper currently has a 31 series deep cycle marine battery i got for $99 at Rural King and it's plenty big enough to get the job done.

It is not guaranteed 105ah@20hr, it is only a suggestion by the manufacturer, for a normal use. The more intense use, the shorter the time before the next recharge of the battery. i.e.: if for 20h, you light up all incandescent lamps, will demand more amperage than if all your lights are LEDs that uses at least 10 times less amps. That will determine the length of time between recharges of your battery.

what a 3.2 amp battery .

Green 666 by isotope rays is NOT forgivable; it leads to permanent hell. 666 is given with World Passport with no name on it (grey plastic card). Police 666 people on highways. Food stores and prisoners/insane asylum folks (released by the antichrist) 666 people too. Reject vaccines. Don't go into UFO to be “healed” by evil demons. Hide with Orthodox Christians to escape 666; leave all electronics behind so that antichrist's minions can't track you; burn documents as documents are from Satan.

Lets say a SLA battery is rated at 20Ah capacity at 20HR. This basically means that the battery can discharge 1 amp per hour over a 20 hour period.

Also, don't get confused with auto batteries that claim very high amperage 'Cold cranking amps'.  The actual current a car starting battery will deliver is based on having to do that for just a few minutes or even seconds, and then the running engine alternator immediately recharging it.  They are not a deep cycle battery.  As noted from others, the battery should supply 5.25 amps continuously over 20 hours, or 10.5amps over 10, it is all just math, but an excessively  high discharge rate can warp plates and ruin the battery, and in actual practice, the heavier load will not follow the math and the battery will go dead faster than you think.

Lets say a SLA battery is rated at 20Ah capacity at 20HR. This basically means that the battery can discharge 1 amp per hour over a 20 hour period.

Pop-up's and rv's use deep cycle car batteries.  It's important that's it's deep cycle otherwise you will kill it.    Basically they are saying you can pull 5.25 amps (105/20)  over 20 hours.    The spec is used on RV's so you can estimate how long you can use it before you need to charge it.  

It is customary to quote battery capacity that way.  

What it means is that the battery can deliver (when new) 

105 / 20 Ah, or about 4.375 amps continuously over a 24 hour period.  

After that, it Must be charged. 

If the draw is less, of course the discharge is also less 

and can be extended over a greater period of time;  

if it is more, the time must be shorter.   

Divide 105 by the actual current drawn,  

which will give you the maximum number of hours for that load.   

It would mean that it rated output is only guaranteed for 20 HRs.