I guess this a pretty common ground cover, I just don't know the common or latin name for it. Surely someone will know this one.
Except for the white flowers, it looks like Western Wild ginger, try searching images for Asarum caudatum?
Thanks Daniel for the latin name, but your link was a little messed up. I did a google search of Maianthemum dilatatum and the common name is false lily of the valley. It's also known as snakeberry, two-leaved Solomon's seal. Was thinking of using it in an urban landscape but after reading more about it, it seems it might be a little more invasive than I would like. Is it really hard to control or is it just a matter of pulling up what you don't want?
I planted some under a cherry tree; and it has spread to cover the entire area, which is enclosed by concrete retaining walls. It works well in this area, but it might be a pain to prevent it from spreading where there is no barrier.
My advice is to be careful. We added a clump of this to a bare area under the huge Douglas fir in my dad's backyard a couple of years ago. The area already had clumps of sword ferms and bigroot geranium which were thriving. I though the Maianthemum would be another nice native addition as it seems to coexist with other understory plants in the wild. After two years it had spread to an area about 6' x 6' and was heading for the lawn. We decided to dig it all out this spring and will be watching closely for any missed sprouts. This soil was quite rich in organic matter with a deep layer of composting needles. The plant might be more restrained in an area with poorer, less loose soil.