Bureaucrats are special users that can assign or design users' special privileges; specifically, to what permissions groups a user belongs to. In other words, a bureaucrat user assigns privileges: they can edit what groups a user belongs to.
To become a bureaucrat is not automatic, and can only be assigned by an existing bureaucrat. This is to protect against malicious actors who could wreak havoc on the system by preventing users from editing content or protecting their own edits. You do not need to be a bureaucrat to edit or create articles: that right is free to anyone, whether a registered user or not.
To see what actions a user may perform, see Special:UserGroupRights.
To see what groups a user belongs to, see Special:UserRights.