XOR Operation Intuition

Question

Except for one, every element in an array of numbers appears twice. 

Locate that solitary one.

Keep in mind that your algorithm should have a linear runtime complexity. 

Could you do that without using any more memory?

class Solution {
public:
    int singleNumber(vector<int>& nums) {
        int result = 0;
        for(auto & c : nums) {
            result ^= c;
        }
        return result;
    }
};

First of all, what sorts of keywords should I be paying attention to in order to figure out that I should be using an XOR operation for this question?

Also, why does XOR'ing all items in the vector with each other give us the one that is not repeated?