Follow-the-cursor eye animation
Programming in German results in an awkward mix of English and German identifiers, with conflicting capitalization conventions.  I suggest sticking to English, though I will make an attempt to accommodate your language preference here.

The code is duplicated not only for each eye, but also for each axis, resulting in four copies.  The copy-and-pasted code is hard to follow because you have pasted them in an order that is not quite parallel:


var abstandV1 = …;
var pupilleL1 = …;
var augeLinks = $("#augeLinks")
var distanceX=…;
var distanceY=…;
if …
var abstandH1 = …;
var pupilleL2 = …;
if …



A more logical order would be:

var augeLinks = $("#augeLinks");
var abstandLY = …;
var pupilleLY = …;
var distanceLY = …;
if …
var abstandLX = …;
var pupilleLX = …;
var distanceLX = …;
if …


Instead of using if-statements the enforce the lower and upper bounds, I suggest using Math.min() and Math.max().



Using the same code for the left and right eyes is easy: just make smarter use of jQuery selectors:

$('.pupille').each(function() {
    var $pupille = $(this);
    var $auge = $(this).closest('.auge');
    …
});


Writing one version of the code for both the horizontal and vertical axes is tricker.  I suggest defining a horizontal and a vertikal object to extract the relevant attributes.



var horizontal = {
    groesse:  function($el) { return $el.width(); },
    position: function($el) { return $el.position().left; },
    offset:   function($el) { return $el.offset().left; },
    cursor:   function(event) { return event.pageX; },
};
var vertikal = {
    groesse:  function($el) { return $el.height(); },
    position: function($el) { return $el.position().top; },
    offset:   function($el) { return $el.offset().top; },
    cursor:   function(event) { return event.pageY; },
};

function koordinate($pupille, $auge, cursor, achse) {
    var augeGroesse = achse.groesse($auge) - achse.groesse($pupille);
    var abstand = achse.cursor(cursor) +
                  achse.position($pupille) -
                  achse.offset($pupille) -
                  achse.groesse($pupille) / 2;
    return Math.max(0, Math.min(augeGroesse, abstand));
}

$(document).on('mousemove', function(event) {
    $('.pupille').each(function() {
        var $pupille = $(this);
        var $auge = $(this).closest('.auge');
        $pupille.css({
            left: koordinate($pupille, $auge, event, horizontal) + 'px',
            top:  koordinate($pupille, $auge, event, vertikal) + 'px',
        });
    });
});
.auge {
  position: relative;
  display: inline-block;
  width: 150px;
  height: 150px;
  border: 10px solid black;
}
.pupille {
  position: absolute;
  top: 50%;
  left: 50%;
  width: 30px;
  height: 30px;
  background-color: blue;
  border-radius: 15px;
}
&lt;script src="https://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"&gt;&lt;/script&gt;
&lt;div id="augeLinks" class="auge"&gt;
  &lt;div id="pupilleLinks" class="pupille"&gt;&lt;/div&gt;
&lt;/div&gt;
&lt;div id="augeRechts" class="auge"&gt;
  &lt;div id="pupilleRechts" class="pupille"&gt;&lt;/div&gt;
&lt;/div&gt;