Length of mid part of the string in Pumping Lemma
Any finite state automaton that accepts an infinite number of words will necessarily have a loop in it. One such loop may go from state $q$ to state $q$ consuming word $y$ – that is, $y$ is the word based on the symbols on the transitions going from $q$ back to $q$. 

The pumping lemma says, more or less, that you can get to such a state $q$ from the initial state by consuming the word $x$ and that you can get to the final state from state $q$ by consuming the word $z$. In the middle you can go through the loop as many times as you like. Thus making the complete word $xy^iz$, where $i$ is the number of times you chose to go through the loop.