Background is a subtype of Enchantments, and flavorfully represents a Commander’s backstory — or at least an aspect of it. They do function as normal enchantments, so if they are in a deck they can be drawn and cast normally, although as they specifically only affect Commanders, it’s very unlikely you’ll ever encounter one in any other format.
But the real interesting bit of Background isn’t the Background cards themselves, but the other cards that reference them. Certain Legendary Creatures will have an ability that reads Choose a Background. That functions as a very specific variation of Partner. If your Commander has Choose a Background, you may choose any one Background card that will essentially function as a second Commander, adding its color identity to your deck, and following the rules of Commander tax and going back to the command zone when it would move from the battlefield to anywhere else.
This also means that if you are able to turn a background into a creature (one that isn’t already a creature, anyway, looking at you Faceless One), then it will be affected by itself. In other words, it will get whatever bonus or ability the Background would grant to any Commander creature you control.
Partner as an ability was a bit problematic, opening up the Commander format a little too much, and becoming more and more powerful the more cards that are printed with it. “Partner with” fixed that problem, limiting the partner option to specific pairings. Background looks to play around in that space a little more, opening up the possibilities a little more than “Partner with” without going full on into Partner territory.
Choose a background for your commander today at cardkingdom.com!