Edit in JSFiddle

$(function() {
    var $move = $(".move");
    
    $(".right").hover(
        //mouseenter
        function() {
            var setWidth = $(window).width() - $(this).innerWidth() - 10;
            
            $(this).prev().css("width", setWidth + "px");
            $(".move").css({
                "top": $(this).offset().top + "px",
                "width": $(this).innerWidth() + "px"
            });
            
        },
        //mouseleave
        function() {
            $(this).prev().css("width", 0);
        }
    );
});

<div id="container">
    <div class="move"></div>
    <ul id="menu">
        <li>
            <div class="side left"><p class="text">Maybe that's what life is... a wink of the eye and wining stars.</p></div>
            <div class="side right"><p class="text">ABOUT</p></div>
        </li>
        <li>
            <div class="side left"><p class="text">Maybe that's what life is... a wink of the eye and wining stars.</p></div>
            <div class="side right"><p class="text">It's Me</p></div>
        </li>
        <li>
            <div class="side left"><p class="text">Maybe that's what life is... a wink of the eye and wining stars.</p></div>
            <div class="side right"><p class="text">Different Size</p></div>
        </li>
        <li>
            <div class="side left"><p class="text">Maybe that's what life is... a wink of the eye and wining stars.</p></div>
            <div class="side right"><p class="text">L</p></div>
        </li>
        <li>
            <div class="side left"><p class="text">Maybe that's what life is... a wink of the eye and wining stars.</p></div>
            <div class="side right"><p class="text">OK yo</p></div>
        </li>
    </ul>
</div>

* {
  margin: 0;
  padding: 0;
}
ul {
  list-style-type: none;
}
html {
  background-color: #444;
}
#container {
  position: absolute;
  top: 0;
  left: 0;
  width: 100%;
  height: 100%;
}
#menu {
  position: relative;
  top: 50px;
  font-size: 0;
}
li {
  position: relative;
  width: 100%;
  height: 50px;
  margin-bottom: 10px;
}
.side {
  position: absolute;
  display: inline-block;
  color: #fff;
  width: auto;
  box-sizing: border-box;
  height: 50px;
  line-height: 40px;
}
.left {
  left: 0;
  font-size: 20px;
  border-radius: 0 8px 8px 0;
  width: 0px;
  overflow: hidden;
  text-align: right;
  background-color: #098ae1;
  transition: width .3s;
}
.left.on {
  width: 500px;
}
.right {
  right: 0;
  font-size: 20px;
  border-radius: 8px 0 0 8px;
}
.text {
  display: inline-block;
  position: relative;
  box-sizing: border-box;
  padding: 5px;
  width: 100%;
  height: 100%;
}
.move {
  position: absolute;
  right: 0;
  border-radius: 8px 0 0 8px;
  background-color: #098ae1;
  width: 0;
  height: 50px;
  transition: all .3s;
}