As the name suggests, this kind of function type are for internal use within the contract. These internal functions can be either library internal functions or functions inherited from the super contract. All of these functions must be executable internally. 

The following example that shows how to use internal function types:

library ArrayIteratorLib {
    function iterate(function(uint) pure returns (uint) _skipFn) 
    internal pure returns (uint[] tempArr) {
        tempArr = new uint[](10);
        for(uint i = 0; i < 10 ; i++) {
            tempArr[i] = _skipFn(i + 1);
        }
    }
}

contract SkipContract {
    function skip1(uint _i) internal pure returns(uint) {
        return _i * 1;
    }

    function skip2(uint _i) internal pure returns(uint) {
        return _i * 2;
    }

    function getSkipFunction(uint _fnNumber) internal pure returns 
    (function(uint) pure returns(uint) ) {
        if(_fnNumber == 1)
            return skip1;
        else if(_fnNumber == 2)
            return skip2;
    }

    //Returns Array[1,2,3,4,5,6,7,8,9,10]
    function getFirst10WithSkip1() public pure returns (uint[]){
        return ArrayIteratorLib.iterate(getSkipFunction(1));
    }

    //Returns Array[2,4,6,8,10,12,14,16,18,20]
    function getFirst10WithSkip2() public pure returns (uint[]){
        return ArrayIteratorLib.iterate(getSkipFunction(2));
    }
}