Yahoo Email Hack - NOT!!
This really isn't a Yahoo! problem. I think the author just wanted to take a shot at Yahoo!.
Since many people reuse passwords for multiple accounts, the hackers were able to use the information to gain entry to Yahoo Mail accounts.
It's a problem I identified years ago, when people were signing up for a service I ran.
You let people sign up for your website, and let them use their email address to identify themselves. Then you ask them for a password. Chances are, they will use the same password everywhere. So now you have their email address and most likely the password to their email address (and Google+, Yahoo!, AOL, and Facebook, etc.)
GENERAL ADVICE: Don't log into service X with your email address from service Y and certainly don't use the same password for both if you do.