Custom backgrounds, or CBGs, are pictures that are either .png, .jpg of .gif format, usually of Super Mario Flash 2 and Super Mario Flash 3's supported resolution of 320 by 240 pixels, that can be used as a level's background if located by URL using Super Mario Flash 2 and Super Mario Flash 3's custom background feature. This allows for level creators to put their own background/theme into their level, allowing for much more creativity. This feature was added in Super Mario Flash's 2.1 update, so only hacks that are at least using 2.1 as base have custom backgrounds supported.
Custom Background Sources
Level Palace Custom Backgrounds
Other Official Sources
Some hacks come with a list of custom backgrounds to be used when you go to their respective page (you can find it by clicking "Play here" next to a game on Level Palace).