Plain English Meaning
This is one of several precision approaches to Runway 28 at a particular airport. The 'Z' is just a label that tells you which version of the ILS approach you are flying, because there is more than one ILS to that runway.
Full Definition
An Instrument Landing System approach procedure to Runway 28, with the letter Z used to distinguish it from one or more other ILS approaches to the same runway. When two or more straight-in instrument approaches of the same type serve the same runway, each is assigned a different letter from the end of the alphabet (Z, Y, X, W, etc.) so pilots and controllers can refer to a specific procedure without confusion.
Context Anchor
Seen at the top of an instrument approach chart and in an approach clearance or when a is preparing to fly that exact procedure.