What is a binary explanatory variable? Can someone provide a simple definition of what a binary explanatory variable is?  A description in simple terms would be ideal.  How would you recognize one?  
 A: A binary variable can assume only two values. Numerically, it is usually represented as 0 or 1.
According to the Wikipedia article:

Often, binary data is used to represent one of two conceptually opposed values, e.g.  
  
  
*
  
*the outcome of an experiment ("success" or "failure")  
  
*the response to a yes-no question ("yes" or "no")  
  
*presence or absence of some feature ("is present" or "is not present")  
  
*the truth or falsehood of a proposition ("true" or "false", "correct" or "incorrect")
  

Explanatory means that a random variable is being used to explain another variable of interest (the response variable). 
The definition of stat.berkeley.edu glossary says:

In regression, the explanatory or independent variable is the one that is supposed to "explain" the other. For example, in examining crop yield versus quantity of fertilizer applied, the quantity of fertilizer would be the explanatory or independent variable, and the crop yield would be the dependent variable. In experiments, the explanatory variable is the one that is manipulated; the one that is observed is the dependent variable.

A common synonym for binary variable is: dummy variable.
