What does the chief arbiter do? The rules of chess are straightforward so I must ask what does the chief arbiter do? what is the difference between him and a regular arbiter?

For example Anand and Carlsen had to meet him behind closed doors before the world championship started.
The chief arbiter is in practice no different from a standard arbiter - it is more a convenience in tournament organization. 

In many tournament there are so many players that it is necessary to have several arbiters, and of those usually the one with the highest title (often IA for professional or large tournaments) is considered the 'chief' arbiter who is responsible as arbiter for all purposes that concern FIDE, etc. and to whom all other arbiters report. This also allows for less experienced arbiters to be used where necessary, as disputes with a less experienced arbiter (unlikely, but possible) can then be taken to the chief arbiter.