Base curve is the actual curvature of the lens as measured from the inside of the lens using an instrument called a lens clock. The flatter the lens, the lower the base curve number. Hence a lens base curve of 6 is "flatter" than a lens base curve of 8.
Some people who wear glasses are extremely sensitive to the base curve of a lens. Having the wrong base curve and throw off an otherwise correct and accurate lens prescription (it has happened to me a couple of times).