I've explained these in writing which is probably easier to understand than the schematic: Pins D2-D9 of the Arduino are connected to pins IO0-IO7 of the EEPROM Pins QA-QH of the first shift register ...

This is a simple circuit for programming ... and control lines of the EEPROM, two 74HC595 shift registers are used for the 11 address lines (15 for the 28C256) and the output enable control line. The ...