"Two quadrant" and "four quadrant" refer to two possible operating modes of a VCA. In two-quadrant operation, when the control voltage goes negative, the VCA remains off. This is the behavior of most standard VCAs. In "four quadrant" operation, when the control voltage goes negative, the gain of the VCA goes up proportional to the absolute value of the control voltage, but the output is inverted relative to the signal input.
In four-quadrant mode, if alternating signals containing no DC offset are presented to both the signal and control inputs, the VCA will act as a ring modulator. In fact, most ring modulation circuits used in synths are based on four-quadrant VCAs, rather than the classic diode-ring circuit (which presents significant design difficulties when used at audio frequencies).