I originate from much more of a Java background. Within the this past year or two, it's become somewhat popular to complete server push over HTTP using long-lived HTTP connections in Comet. This is an very helpful technique.

So I am curious exactly what the equivalent is by using Apache + PHP + Javascript? One option I see is simply using straight AJAX calls (eg with jQuery) however i don't fully realize how Apache handles them or the way i can use this type of factor around the serverside with PHP. Any ideas? Worthwhile assets about this type of factor?

You should use Comet programming approaches to PHP. I believe a great starting point is post, explaining how you can implement Comet in PHP.