How can I change image source on click with jQuery?

You need to use preventDefault() to make it so the link does not go through when u click on it:

fiddle: http://jsfiddle.net/maniator/Sevdm/

$(function() {
 $('.menulink').click(function(e){
     e.preventDefault();
   $("#bg").attr('src',"img/picture1.jpg");
 });
});

It switches back because by default, when you click a link, it follows the link and loads the page. In your case, you don't want that. You can prevent it either by doing e.preventDefault(); (like Neal mentioned) or by returning false :

$(function() {
 $('.menulink').click(function(){
   $("#bg").attr('src',"img/picture1.jpg");
   return false;
 });
});

Interesting question on the differences between prevent default and return false.

In this case, return false will work just fine because the event doesn't need to be propagated.