My basic mental model of SETF was always relatively simple. We were told that in university, many decades ago.

Lisp has traditionally a bunch of different datastructures. Like cons cells with CAR and CDR accessors. RPLACA and RPLACD were the setters, from a time when characters were expensive, so that identifiers were short and abbreviated (RPLACA would be short for Replace CAR). Then there were property lists with accessors GET (-> Maclisp) or GETPROP (-> Interlisp). The setter was PUTPROP.

So for any datastructure we need to learn both a getter and the corresponding setter.

With SETF in Common Lisp we only need to know the getter. SETF knows for each getter a corresponding setter.

So for a datastructure FOO we don't need to know both GETBAR and BARSET!.

The getter is (GETBAR SOMEFOO) and the setter is (SETF (GETBAR SOMEFOO) SOMETHINGNEW). SETF then is a macro which knows how to set the thing.

Advantage: we don't have to learn ancient functions like RPLACA with calls like (RPLACA CELL 42), but we can write (SETF (CAR CELL) 42). Take the accessor and wrap a SETF around it, include the form for the new value.

In reality there is a bit more magic involved.