The way permissions are set-up on different wikis can vary, but the default MediaWiki installation has several different permissions available; most notably the sysop and bureaucrat permissions.

Soft security - There are no permissions

Wikis are often set up to be freely and openly editable. This means anyone can edit the pages, often without even registering/logging in. This is only possible because wikis offer a unique kind of "soft security". By making it very simple to monitor edits, and revert changes to retrieve an older version of a page, a wiki does not need to be very restrictive at all.

There are no permissions. Everyone is an administrator. You do not need permission to edit, and you are encouraged to "be bold", go forth and edit!

...at least in theory. In practice MediaWiki software does offer many options related to permissions.

Sysops

Main page: Scratch Wiki:Administrators

By default MediaWiki provides extra functionality to a group of trusted users called "sysops" (short for "system operators"), known more generally as "administrators" or "admins" for short. Most of the time this should go largely unnoticed by the normal users of a wiki community. Everyone can get involved in editing pages, and even undertaking drastic reorganisation of the wiki. The extra powers of a sysop user are intended for use in settling disputes and preventing repeated vandalism.

Who are the sysops?

You can find out who the sysops are at Special:ListUsers/sysop.

What can a sysop do?

There are a number of extra features available to sysops. The key things they can do are as follows:

Protect and unprotect pages, and edit protected pages
Protecting a page prevents normal users from editing the page at all. There are several reasons why a particular page might be protected. For more information see Help:Protected pages. For sysop information see Help:Protecting and unprotecting pages
Delete and undelete pages
A page can be deleted semi-permanently, such that it is no longer available (even in the page histories) for normal users. Normal users do not have this power. See Help:Deleting a page. For sysop information see Help:Sysop deleting and undeleting
Patrol edits, and see whether edits have been patrolled
Patrolling is a way of coordinating with other sysops, to ensure that every edit of the wiki has been checked over by a trusted user. See Help:Patrolled edits

Bureaucrats

Main page: Scratch Wiki:Bureaucrats

Another level of permissions within a default MediaWiki set-up, is the 'bureaucrat' group.

Who are the bureaucrats?

You can find out who are bureaucrats at Special:ListUsers/bureaucrat.

What can a bureaucrat do?

The main thing a bureaucrat can do, which 'sysop' cannot, is change users' usergroups and block users from the wiki. See Help:Assigning permissions and Help:Blocking users.