Plain English Meaning
The instrument the pilot looks at first to check whether the wings are level or how steeply the aircraft is banked into a turn.
Full Definition
On an electronic flight display, the primary bank instrument is the one that gives the pilot the most direct and immediate indication of the aircraft's bank angle for a given flight condition. In straight-and-level flight and in standard-rate turns, the primary bank instrument is the attitude indicator on the Primary Flight Display, supplemented by the heading indication and the turn rate indicator.