Selector targets overly obtuse - recommendations?
You can certainly cache the lookups, abusing of the scopes.

$(".button").each(function(){
  var $btn = $(this);
  var $box = $btn.parent().children(".innerBox");
  $btn.toggle(function(){
    $box.fadeIn();
  }, function(){
    $box.fadeOut();
  });
});


Using .fadeToggle() instead of .fadeIn() and .fadeOut().

$(".button").each(function(){
  var $btn = $(this);
  var $box = $btn.parent().children(".innerBox");
  $btn.click(function(){
    $box.fadeToggle();
  });
});


And last but not least, .siblings().

$(".button").each(function(){
  var $btn = $(this);
  var $box = $btn.siblings(".innerBox");
  $btn.click(function(){
    $box.fadeToggle();
  });
});