Ban
if someone is hacking and kicking or banning people from the server or spamming that website thing that bans peoples ip's from being able to do certain things.

give them server groups
if someone just got promoted to a new rank and they don't have the icon for in teamspeak then i would be able to give them the rank.

kick
someone on ts is mic spamming the staff member proceeds to kick the member

Join Spacers
Teamspeak staff can join spacers and other channels that have a full limit. They could use spaceers to answer someones questions or if they needed speaking to by a high ranked staff member

Lock channel
You can lock channels with a password and EDIT channels if someone wanted to be left alone

Delete Avatar
This is a power which may be needed, it will remove a player's avatar from their Teamspeak account for when it is unnecessary.
A user has an offensive avatar, a staff member should proceed to ban them.

Granting Talk Power
Allows one person to talk at a time
Example There are 30 people at a meeting, and they are all talking at once,
TS3 staff force mute them all and only let one speak at a time

Moving People
As stratiic pointed out it is one of the most essential things in the world of TeamSpeak
you can move people to different channels its self explanitory