I think that the role of moderators in this forum is not much different from the role of moderators in many other forums. You can refer to Wikipedia to understand what the moderators are responsible for:
Moderators
The moderators (short singular form: "mod") are users (or employees) of the forum who are granted access to the posts and threads of all members for the purpose of moderating discussion (similar to arbitration) and also keeping the forum clean (neutralizing spam and spambots etc.). Moderators also answer users' concerns about the forum, general questions, as well as respond to specific complaints. Common privileges of moderators include: deleting, merging, moving, and splitting of posts and threads, locking, renaming, stickying of threads, banning, unbanning, suspending, unsuspending, warning the members, or adding, editing, and removing the polls of threads. "Junior Modding", "Backseat Modding", or "Forum copping" can refer negatively to the behavior of ordinary users who take a moderator-like tone in criticizing other members.
Essentially, it is the duty of the moderator to manage the day-to-day affairs of a forum or board as it applies to the stream of user contributions and interactions. The relative effectiveness of this user management directly impacts the quality of a forum in general, its appeal, and its usefulness as a community of interrelated users.
Source:
https://en.wikipedia.org/wiki/Internet_forum#ModeratorsUpdate: Also moderators Bitcointalk responsible for the ban of users who violate these rules: