What does the underscore mean in this case?

_ is a placeholder. It means that the values assigned to _ are ignored.

Xcode's migration tool made this changes because it has detected that you didn't use source or myArray anywhere, thus replaced these variables by the placeholder.

Now instead of being assigned to a variable, the returning result of segue.sourceViewController as! RhymeViewController and the returning result of [String]() are ignored.

The returning result is ignored but the expression is still evaluated at runtime: if it has side effects, these effects will occur.

So if you actually don't need these instructions you should get rid of them entirely.