This is really easy with a bit of jQuery.
CSS
div.Message{
    display:none;
}
HTML
<div class="Welcome">Welcome to our site<div>
<div class="Message">Thanks for touching me!<div>
jQuery
$('.Welcome').hover(
    function () {
    $('.Message').show();
  }, 
    function () {
    $('.Message').hide();
  }
);
Example: http://jsfiddle.net/gxn34/
EDIT
To answer your question below
You would need to add the following to your page, usually in the <head> section
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
And 
 <script>
     $(document).ready(function(){
        $('.Welcome').hover(
            function () {
        $('.Message').show();
          }, 
            function () {
        $('.Message').hide();
          }
        );
     });
 </script>