Here was the original thoughts on Local Rules. Way before my time but seems like the idea behind them hasn't changed.
If the topic post of a topic gives very specific rules for the topic, I will use those rules in addition to the global board policies for that topic. The starter of the topic may not change rules after posting their topic (not even by editing the topic post). Local rules can't specify punishments, though people may be banned for breaking local rules too much.
The rules must be specific enough that it takes less than a few seconds to decide whether a post breaks them. When you report posts like these, you must quote the local rule that was broken. Rules will be ignored if they are not specific enough, or if it takes too much work to enforce them.
It is possible for someone to create a "ruleset" that others can quickly apply to their topics by clearly linking to the ruleset.
(It has always been my policy to enforce local rules, though not many people have created topics with such rules.)
For a more recent addition and clarification on the intended use here is one from a locked topic
Local rules are enforced entirely at the discretion of the relevant moderators. It's intended to be for stuff like "you must post a picture", "you must make a price prediction", "do not go on tangents about services other than <this one I'm interested in>", etc. Not really "these people are banned: ...". (Though I have been thinking about adding a function to ban specific users from your selfmod threads.)
Overall it's not meant to hinder any discussion. I see it as a way to create a certain environment for your topic, whether it be a focused discussion, a giveaway/contest or a general fun thread. Where there is a central point or theme that needs to be followed or used as a guide to participate in the intended way.