A pure function is one which do not affect anything outside of it's own scope. This means it may read global variables or variables to which it was passed a pointer but it may not write to such variables. It should not read from volatile variables or external resources (such as files).
const is a stricter version of pure, it tells GCC that a function will not read any data other that of variables that are passed to it. Data cannot be read by dereferencing a pointer passed to a const function.
The only effect a pure or const function can have on your program is it's return value. Having such a function return void would make it pointless.
GCC can use this information to perform common subexpression elimination (!). This means it may call the function fewer times than it was told to as it knows the outcome will be the same each time. For example: if you had a function which converted Celsius to Fahrenheit, and it was placed in a loop calculating the same value each time, GCC would could replace this function call with the value returned. GCC knows this is safe if the conversion function is const.