Snowdrop, or Galanthus nivalis. The latin binomial comes from gala (milk), anthus (flower), and nivalis (of the snow). Lovely.
Unlike the crocus (January 27th) which grows from a corm, or swollen stem base, the common snowdrop grows from a bulb, or swollen leaf-bases.
The flower is made up of apparently six petals, but in fact three are petals and three are sepals. Collectively they are the tepals of the perianth.
Like orchids, they are part of the Asparagales order of the monocot clade. Lots of useful plants are in this order, such as the onions, asparagus (suprise!), garlic and vanilla, but there is a more important order in the monocot clade (guess).
They contain a chemical that has been named galantamine which has been used in the treatment of Alzheimer's disease and vascular dementia and also by people trying to have out-of-body experiences. (It's essentially a mild anti-cholinesterase with additional nicotinic receptor agonist activity.)
The other thing about snowdrops is that there is a thriving market in the various cultivars. It's a bit like the tulip-mania which gripped seventeenth century Holland, with people paying £360 for a single bulb! (Follow the link to an eye-opening BBC article about the craze.)