The push session means that when someones messages you, or replies to one of your messages, you get a pop up box (a push message from a remote server), alerting you to the message. This means once you've logged in via IM+ you can close the app, and you will be alerted if anyone wants to talk to you.
I actually like IM+ more than I like eBuddy, which I was using on my iPhone. Currently I'm also using the "Lite" version, but am considering paying for the full version just to encourage the developers.