MySQL performance is largely defined by keys and how efficiently queries can use them. As you scale, at certain point it isn't enough anymore to just have any indexes and still get a good performance in return. You have to really figure them out and allow your queries to do less work, as little work as possible.
The approach presented in this article can sometimes help designing such good, efficient indexes. As a consultant, I have to rely on it myself from time to time, having to optimize a query that works in a database I know nothing about.