True to the name, action menu dropdowns are used to take action on a specific item within a list of items. They are always used with lists of people or on a row within a table, and are accompanied by a batch action dropdown at the top of the list.

When to use the action menu
In general the action menu should not be used to just tuck away any link. It should be limited to internal actions (add/remove from list, delete, add/remove as a follower),or the type of actions that can be done in batch when views allow for an action menu at the top of a list (add everyone to a list, etc).