2 / 4 quadrant switches - how can current have opposite direction to voltage?
This answer is specific to thyristor / triac operation. I can see from @Cristobol's answer that another meaning can be taken from your question.



Figure 1. From Littlefuse's Fundamental Characteristics of Thyristors.

The Littlefuse diagram makes it clear that the voltage in question is the gate voltage relative to MT1. The article goes on to say ...


  The most common quadrants for Triac gating-on are
  Quadrants I and III, where the gate supply is synchronized
  with the main terminal supply (gate positive -- MT2 positive,
  gate negative -- MT2 negative). Gate sensitivity of Triacs is
  most optimum in Quadrants I and III due to the inherent
  Thyristor chip construction. If Quadrants I and III cannot be
  used, the next best operating modes are Quadrants II and
  III where the gate has a negative polarity supply with an AC
  main terminal supply. Typically, Quadrant II is approximately
  equal in gate sensitivity to Quadrant I; however, latching
  current sensitivity in Quadrant II is lowest. Therefore, it is
  difficult for Triacs to latch on in Quadrant II when the main
  terminal current supply is very low in value.


They're basically saying that if MT2 is positive then a positive gate voltage will work best (QI). If MT2 is negative then a negative gate voltage will work best (QIII).

The application note is well worth reading.