explain nested for_loop and vector.size()

Question

I'm new to C++ and I can't understand this code. It's really hard. Can someone please explain this to me?

#include <vector>
using namespace std;

int calculate_pairs(vector<int> vec) {
    //----WRITE YOUR CODE BELOW THIS LINE----
    int result{};
    for(size_t i = 0; i < vec.size(); ++i)
        for(size_t j = i + 1; j < vec.size(); ++j) /* what is size_t and vec.size? what does this do j = i + 1;*/
            result = result + vec.at(i) * vec.at(j); /*what does this do?*/
    return result;
}