Orchids belong to an Alliance because they are a group of genera sharing characteristics that can interbreed. Examples: Vanda Alliance includes Vanda, Ascocentrum and Rhyncbostylis. The Cattleya Alliance includes Cattleya, Laelia, Brssavola and Sophronitis. Similar situation for Oncidium Alliance. So your chid is a cross between a Cattleya and Brassavola hence the abbreviation "Bc". I'm sure other will be able to give a more complete answer.....