volatile is a keyword known as a variable qualifier, it is usually used before the datatype of a variable, to modify the way in which the compiler and subsequent program treats the variable.
Declaring a variable volatile is a directive to the compiler. The compiler is software which translates your C/C++ code into the machine code, which are the real instructions for the Atmega chip in the Arduino.
Specifically, it directs the compiler to load the variable from RAM and not from a storage register, which is a temporary memory location where program variables are stored and manipulated. Under certain conditions, the value for a variable stored in registers can be inaccurate.
A variable should be declared volatile whenever its value can be changed by something beyond the control of the code section in which it appears, such as a concurrently executing thread. In the Arduino, the only place that this is likely to occur is in sections of code associated with interrupts, called an interrupt service routine.