As a Moderator, you inherit all of the abilities and responsibilities of a Curator. The primary difference is that you are trusted to directly resolve issues with players. That could be banning a player, teleporting them somewhere, investigating griefing/theft and more.
In addition, Moderators are the leaders of their team, and so are responsible for training new and old staff, ensuring they have everything they need to succeed, keeping track of individual progress, maintaining general oversight over their district, and more.
Due to their increased permissions, a moderator truly has the power to tip the balance on the server if their powers are used in a malicious way. Please be careful and thoughtful when using any command that impacts another player.