It's a pinout diagram.

http://en.wikipedia.org/wiki/Pinout

http://en.wikipedia.org/wiki/Circuit_diagram

The numbers on the outside lines of the PIA are the pin numbers. The number/letter code on the inside of the PIA are the functions of each pin. You may need to look at a spec sheet for the chip to determine exactly what the function of each pin is, or a detailed write-up in plain english elsewhere if you are unfamiliar with spec sheets.

In the empty space in the middle of the chip, there's a few additional numbers. The large U14 number is simply the position of the chip on the board. Most ICs are labeled with a U followed by a number. The PIA 6821 tells you what kind of chip it is.

http://en.wikipedia.org/wiki/Peripheral_Interface_Adapter

The positions of the pins in the schematic don't always correspond to a particular function, so don't rely on that for determining what they are. You will have to read the function label and follow the path of the pin to determine that. The pins are simply arranged in a way so that they will fit on the schematic, but in a logical fashion in relation to other components.

I'm not sure of all the definitions off the top of my head, but the "D"s are all Data line inputs. All the "Px"s are data outputs. These should all be pulsing when tested with a logic probe if the chip/board is functioning properly.

CS1 is "Chip Select 1" and is active when HI.

NOT CS2 (CS2 with a line over it) is "Chip Select 2" and is active when LO, identified by the line over it. Any designation with a line over it is a "NOT" signal that is active LO.

6821 data sheet here:
http://pdf1.alldatasheet.com/datasheet-pdf/view/4150/MOTOROLA/6821.html

Signal funtions/names listed throughout.

Its a great read. People sometimes think chips are simple but not so much.

I have seen datasheets for processors and custom logic ICs go for 160 pages sometimes.