Many herbs are useful enough to deserve some dedicated space out in the yard, and this pretty purple flower is one of the herbs I give space to; it is a saffron crocus. The saffron crocus in the picture has come up in a space other than the one I planted it in, the way bulbs do around here. It is under a blueberry bush, along with a whole lot of sheep-sorrel that I need to pull up!
One great feature of the saffron crocus is that, in my yard anyway, it appears around Halloween, reliably, when other plants are shutting down and turning into masses of dead foliage. The flowers are a welcome sight.
The parts used in cooking are the stigmas, the three, bright red, thread-like bits that are the female parts inside each flower. To harvest, I just pick the stigmas out by hand and dry them on a paper towel for a few days before storing.
The plant itself really is a type of crocus, growing from similar corms, with similar planting depth and spacing, and it does best in zones 6-8 here in the Southeast. In colder areas, the corms might not survive the winter. The White Flower Farms website shows that, in the Western U.S., the best growing zones are 6-9.
I tend to think of saffron as a Mediterranean, near-Eastern, and Asian spice, but this article from the Kitchen Gardener magazine archive made available through the Vegetable Gardener website explains that saffron has been used in Lancaster County, PA, for a very long time as an important ingredient in many foods—one familiar example is chicken potpie.