Multiple SUM meaning

Question

Can you please help me to expand this? What I know at the moment is that this part:

Creates one number as the output. What the other sum function does?

Answer 1

$\sum_{i = 1}^n\sum_{j = 1}^m (y_j^i)$ = $y_1^1 + y_2^1 + ... +y_m^1 + y_1^2 + y_2^2 + ...+y_m^2 + ... +y_1^n + y_2^n + ...+y_m^n$

You basically iterate over the inner sum first. Once you have finished that, increment the other index and iterate over the inner sum again. Keep doing this until you have exhausted all indices.

Answer 2

The inner sum creates one number for each fixed index $\mu$. Then you sum over the possible values of $\mu$.