Topic Actions is a small feature to enhance user interaction. They allow administrators to setup a forum in such a way that topics have actionable states that change at the discretion of that topics owner.
Say you setup a question-answer forum on your board. Users come in and post their question as a new topic. When a new topic is created it is put into an "Unresolved" status. As users post, eventually an answer is submitted that the topic owner is satisfied with. Once this happens the owner selects this post as "Accepted" and the topic status moves from "Unresolved" to "Resolved". While waiting for an acceptable answer, users will undoubtedly post things the owner feels are unsatisfactory which can be marked as such (Rejected/Needs Work).
Now for some details. When a board administrator is setting up a forum they should be presented with an "Actions" section. Here, they can set the "Initial State" of topics (Unresolved/Open/Available/etc..) as well as the individual "Post States" (Accepted/Rejected/Needs Improvement/etc..).
Each "Post State" will have an associated color. This changes the color of a posts background container when its state changes.
The "Post States" can be optionally toggled to update the topics status to that state (1 or more states must be selected).
Selected states can also have an optional action, (lock topic/move topic/remove topic?).
The topic owner should be allowed to change the state of a post at any time and changing the state of a post will revert any action of the previous selected state (unlock topic/move topic back to original location).
A topics current state should also be clearly visible when browsing through the topic listings on a forum.
Another example would again bring us to a buy/sell/trade section on an administrators board. A user posting an item for sale would display their topic as "Item Available". Users making low-ball offers could have their posts set to a "Rejected" status. Once a reasonable offer comes along it can be marked as "Offer Accepted" and the topic locked. The topic will then show "Offer Accepted" to anyone browsing that forum. Once the trade is completed the seller can come back and swap the post from "Offer Accepted" over to "Sold" and the topic could be automatically moved into a "Sold Items" subforum.
There are probably many more use-cases for this, especially since the states can be customized, each post can have a changing state, and states can have optional actions. A board administrator is only limited by their creativity at this point.
All-in-all this feature promotes intractability between users and the ability for them to take on a role in keeping the forums clean and tidy along with saving their time by displaying pertinent information at a glance where it is needed most.