BSC stands for Baffle Step Compensation.
Imagine a 6½" woofer in a rectangular 9" wide cabinet. Sound with wavelengths longer than than 9" tends to wrap around the edges of the cabinet. And sound with wavelengths shorter than 9" tend to reflect off of the front baffle. As a result, the longer wavelengths will be quieter than the shorter wavelengths.
Unless there is compensation for this, the sound will be noticeably louder in a region of the mid range. It can make voices and instruments sound a bit forward, nasal, 'shouty', or 'honky'. This louder frequency range is called the Baffle Step – because frequency response curves often show a range where the loudness is stepped up.
In speakers with passive crossovers, the baffle step should be compensated, or equalized, to level out the frequency response across the baffle step region. It's done by reducing the loudness across the baffle step region until it's about the same level as the bass below it. You cannot raise loudness in a passive crossover, you can only lower it. These circuits are called BSC circuits, and they reduce a speaker's sensitivity, requiring more power and more current across the affected frequencies.
Here is an example recently posted by rojo. See the region labeled 'Forward Image'. The baffle step starts above 1 kHz and continues to nearly 3 kHz. That's caused by a speaker without enough Baffle Step Compensation.