This is basically one way of saying that if the number if not null or undefined
if(+!!variableName)
  doSomething();
if variableName is 0,  empty (""), null or undefined, it will translate to false or else to true.
For example, if
var variableName = null;
now, this will translate to (+!!null) -> (+!true) -> (+false) -> false
similarly, if 
var variableName = "anything";
This will translate to (+!!"anything") -> (+!false) -> (+true) -> true
+ in this case has no effect on the outcome, so can be safely removed.
In fact, whole conditional expression can be replaced by
if(variableName)
  doSomething();