A user account with permissions to perform administrative actions within an operating system or application.
Related tag: privilege-escalation.
On Windows, administrative actions are protected by the User Account Control (UAC) feature. A "privileged account" is one that has one or more admin powers within the UAC framework.
On Linux, OS X, and other Unix variants, a "privileged account" is either root or an account with rights to use sudo.
An application can have privileged accounts such as admin that are capable of special functions like user account administration or unrestricted data alteration.