How do wafers translate to computer hardware?
Semiconductor chips are not fabricated individually.  It is more efficient to create a whole bunch at a time from one large slab of silicon, then break it apart into individual chips later.  That slab is called a wafer.

After a chip is separated from the wafer, it is put into a package so that the chip itself is enscased and protected from the elements.  Only those nodes intended to be connected to externally are wired out of the package via its pins.  This whole assembly is then often referred to as a "chip", since it is a single unit from this point forwards.

Multiple chips and other electronic components are then soldered to a circuit board, wired to some external parts like the power supply and front panel buttons, encased in a chassis, etc, to make a whole computer.