Like dried flowers in a storebought display, California everlasting has crispy, white, straw-like petals. But actually these petals are bracts – you have to look close, and at the right time, to see the real (yellow) petals peeking through from the flower inside. When done flowering, the bracts open wide around a dandelion-like puff of seeds. 
Pseudognaphalium californicum is a native that’s found in most parts of North America. It’s in the Asteraceae family, along with dandelion, chamomile, burdock and daisy. It dries out as nicely as its name suggests!
There are several similar-looking species to this one, including others in the Pseudognaphalium family. But I first mistook this plant for the very similar lookalike: pearly everlasting (Anaphalis margaritaceae – thanks to Doreen for setting me straight!). I’m still trying to figure out a good way to tell the two apart – in the key, the main difference is that California everlasting has a taproot while the roots of pearly everlasting are fibrous. I think that the flowers of the first are either bisexual (a typical flower, with both male and female parts) or only female, while the latter has separate male and female flowers. But since they are in the aster family, with little teeny tiny flowers, this is a hard difference to spot.
Just from looking at the photos, it seems that California everlasting has a much sleeker, smoother look to the shape of the bracts, while pearly everlasting seems to have a spiky look to each flower head, with the many pointy tips of the bracts bent backwards a little bit.
I’ll offer more tips on how to tell these two apart, as I come up with them!