ExGFX is Extended Graphics that can be added to Super Mario World via Lunar Magic. The purpose of using ExGFX is to be able to use new graphics without overwriting Super Mario World's original graphics. It can also be used to fit certain combinations of enemies from different tilesets into one level.
A popular ExGFX editing/making tool is YY-CHR, though ExGFX can actually be made within Lunar Magic. It's a "mask" that can replace FG/BG graphics, as well as sprite graphics. Most ExGFX files need to be assembled in Map16 pages, since they don't use the same Map16 arrangement as the original SMW tiles (though some do).
SMW Central has a database specifically for Hosting ExGFX. It currently has well over 1000 ExGFX files.
EXGFX can be extracted from a Super Mario World ROM in Lunar Magic by clicking the Purple Mushroom, and can be inserted by clicking the Yellow Mushroom.