Writing and Reading data from RTC module EEPROM_Arduino
These two lines write a 16 bit (2 8-bit) value, which is signed -32768..32767 or unsigned 0..65535.

Assume a value in bits: 10101010 11001100

Statement 1: 

Wire.write((int)(eeaddress &gt;&gt; 8)); // MSB


The first statement shifts the value 8 bits (positions) to the right; this is called the MSB (Most Significant Byte, the left 8 bits). Bits on the right are clipped / fall off. Thus

10101010 11001100


will become

00000000 10101010


When casted to an 8 bit value you get:

10101010


Statement 2:

Wire.write((int)(eeaddress &amp; 0xFF)); // LSB


The second statement will get the LSB (Least Significant Byte). This used the AND operator, meaning a bit is only 1 if both values are 1. 0xFF is the 'mask'

Original value: 10101010 11001100
Mask:           00000000 11111111
                ----------------- AND (&amp;) operator
Result:         00000000 11001100


As you can see only the right 8 bits are kept. When casting this to an 8 bit value:

11001100