If you have a huge training set with 5000000 training samples, $X=[ x^{(1)}, x^{(2)} ,..., x^{(5000000)}]$ Let's say each of your baby training sets have just 1,000 examples each. So, you take the first mini-batch as $X^{\{ 1\}} =[x^{(1)}, x^{(2)} ,..., x^{(1000)}]$. And then you take home the next 1,000 samples $X^{\{2\}} =[x^{(1001)}, ..., x^{(2000)}]$ and so on.

Altogether you would have 5,000 of these mini-batches and then similarly you do the same thing for Y. Hence we end up with mini-batches $X^{\{ T\}}, Y^{\{ T\}}$, T = 1,2...,5000.