Is there multiple ways to cin vector elements?

I have a program that adds multiple vectors in 1 vector. I saw a method of instead of .push_back to add elements and I used it, but I am wondering why this works because I thought vector[] indicated the index, so why is cin >> vector[] adding elements into the vector if square brackets indicate the index?
input – output
1 2; 5 4; 9 1 – 1 2; 5 4; 9 1

'''
    #include <vector>
    #include <iostream>
    using namespace std;
    int main()
    {
    int q = 3; //total number of q2 in q1
    vector<vector<int>> q1; //vector for q2's
        for(int a = 0; a < q; a++)
            {
            vector<int> q2(2); //making each q2 vector the size of 2 elements
            for(int b = 0; b < 2; b++){
                cin >> q2[b]; //adding elements to q2**how does this work instead of push_back?
                }
            q1.push_back(q2); //adding last q2 into q1
            }
    //printing q1
        for(int a = 0; a < q1.size(); a++){
            for(int b = 0; b < q1[a].size(); b++){
                cout << q1[a][b] << " ";
                }
            cout << endl;
            }
    }
'''