JQuery show and hide div on mouse click (animate)

That .toggle() method was removed from jQuery in version 1.9. You can do this instead:

$(document).ready(function() {
    $('#showmenu').click(function() {
            $('.menu').slideToggle("fast");
    });
});

Demo: http://jsfiddle.net/APA2S/1/

…but as with the code in your question that would slide up or down. To slide left or right you can do the following:

$(document).ready(function() {
    $('#showmenu').click(function() {
         $('.menu').toggle("slide");
    });
});

Demo: http://jsfiddle.net/APA2S/2/

Noting that this requires jQuery-UI’s slide effect, but you added that tag to your question so I assume that is OK.