usage of at24c02 eeprom with ethernet module
A MAC address is a unique address every single Ethernet node has. It is a six byte address, the top three bytes of which are a manufacturer's unique ID and the bottom three bytes of which are a serial number. These number are used as source and destination addresses when sending Ethernet packets. 

When you start to manufacture device with Ethernet ports you are supposed to register with the IEEE who will issue you with your manufacturer's ID which will not change. Then, as you manufacture devices, starting at 0, you will work your way up to 0xFFFFFF. You will usually see these numbers written as bytes separated by a colon. So, your first device would be MM:MM:MM:00:00:00 where MM:MM:MM is your three byte manufacturer's number. Your next would then be  MM:MM:MM:00:00:01 and so on. 

If you manufacture HUGE numbers of devices you'll eventually run out and need to buy a new manufacturer's ID. 

Now, you need to store this MAC address in your product, so a little EEPROM with a few bytes of data is ideal for this.