A revenue sharing forum shares earnings with its members since without members there wouldn't be a forum. This is typically done with some kind of affiliate program such as Google AdSense. There would be AdSense advert blocks around the forum. If you reply in a topic you will be entered in a rotator of who's AdSense block shows up and you will earn some of the revenue coming from that topic.

It can also be done by paid to post. Paid to posts typically pay every month. They take total earnings and choose a percent of it that gets paid to members. Once they know how much they want to pay to members they divide that number by the number of posts. Then they award each member money or points for each post that they have.

You must have an AdSense account through Google.

You must have at least 50 total posts within the forum to participate (once you reach that level, the ads displayed from that point forward are retroactively applied to all the threads you started or participated in).

For threads you start, your AdSense client ID will be used 50% of the time when the thread is viewed as a thread.

Your AdSense client ID will be used 50% of the time when the thread is viewed by post (and you made the post).

Above are some of the restrictions for participating in revenue sharing.