Something that's filmy is light and translucent. Filmy white curtains are especially pretty when the sun shines through them and they blow in the breeze.
The adjective filmy often describes fabric that you can almost see through, like a filmy dress you wear to the prom. A filmy layer of light might rest on the surface of water, and your old dog might have filmy eyes. In all of these examples, the filmy thing is nearly as thin as a film or membrane: the word stems from the Old English filmen, "membrane or thin skin."