B.B. stands for Beauty Balm although in Smashbox's case it should stand for Beauty Bomb (as in, it's da!).
Originally called Blemish Balm and developed in 1960s Germany for dermatology patients after surgery, the cream was discovered by Korean actresses around 1985. They loved the lightening affects and sheer coverage. The products have remained very popular in South Korea and Japan ever since. As best as I can tell, they only entered the mainstream US market in 2011.
It is a skin care meets make up hybrid promising to replace moisturizer, primer, sunscreen, foundation and powder (the last two depending on the amount of coverage you want). I tried a Garnier brand when they first came out but it made my face greasy and was immediately returned. I bought the Smashbox while shopping with a friend in Light/Medium. I absolutely love it. I think it does everything it claims. My face is moisturized, my skin tone more even, and it keeps my face from getting too shiny all day long only without a matte finish which, let's face it, isn't really a natural look. After only a couple of weeks, my slight tan faded and I ordered it in Light. I would say the biggest problem is that it is only offered in 5 shades. Although both shades I have work because they blend really well. Sometimes this is all I use and on the occasions when I do wear more make up, I use a dusting of Tarte Smooth Operator to help set the other make up.
There are many brands out there in a range of prices but unless this stops working, I will consider myself lucky that I found this on only my second try.