THIS IS A PLANT TO USE IN QUANTITY. It's a Claytonia or Montia, one of a group in the Purslane family that are often referred to as springbeauty for their habit of producing clouds of white or pink flowers in the spring.
Perhaps the most famous of these is Claytonia perfoliata (pictured above), an annual native plant of the West (from Alaska to California from the Coast to Utah) that became known as "miner's lettuce" because, during the Gold Rush, vegetable-deprived miners relied on this common plant for badly needed nutrients. It can be eaten raw in salads or cooked like spinach and is high in Vitamin C, Vitamin A, and iron.
However, there are native Claytonias for almost everyone. (The Native Plant Information Network lists 12 of them.) Where I live, our springbeauty is C. caroliniana, aka Carolina springbeauty, which ranges from Newfoundland to Ontario and as far south as Tennesee. This is a particularly pretty one, with pink or white flowers that have visible pink veins. It is perennial, with tuberous roots that can be eaten like potatoes.
What the Claytonias all seem to have in common is a mounding habit, growing as tall as a foot and equally as wide. Rich green foliage is topped by small flowers in spring.
The Claytonias are useful garden plants if you want coverage for moist, shady areas. Just give them loose soil and make sure they're watered.
But they are phenomenal garden plants if you have room to use them in quantity. A carpet of Claytonia, with its rich green foliage and mist of tiny flowers, is truly a lovely sight. Think of it as a replacement--and improvement upon--lawn for any shady spot.