Around here it's called a Poor Man's Orchid. I've seen it also been referred to as Australian Fairy Iris. I like that! More commonly, African Iris, (Moraea grandiflora).
It's a common "filler" plant. People plant them just to fill space in their gardens. But they are not noticed much amongst the long spiky leaves and everything else that grows abundantly here in California.
When I took this picture, it was late in the day and the flower didn't show up very well. But after cropping everything else out and just the flower sat there in the shading it's fragile beauty struck me. It's like candy. So sweet. I've heard the expression "eye candy" before, usually in relationship to handsome boys or pretty girls to be admired. But, this was candy for my wounded soul (a spoonful of sugar makes the medicine go down).