Apple started off making computers (or maybe "integrated hardware/software experiences" is a better way to put it). After their comeback, they still made computers. Now their big thing is portable computers -- a big change, but still related to what they always did. Their focus is on design and UX expertise.
Yahoo started off making a hierarchical directory of web sites, then dove into the web portal craze of the late 1990s. After their comeback, they will ___________. Their focus is on ___________.
Fill in the blanks. It's not going to be what they did before, because nobody wants more hierarchical web directories and portals. They have a bunch of people still using their webmail, so that's one option. GMail wiped the floor with them before, but it's been getting clunky lately thanks to G+. Yahoo could try to recapture the clean simplicity of Google's early days. That would be a big challenge indeed -- as a portal company, the idea of leaving blank space on a web page is utterly alien to them.
It looks like they're producing independent news. That's an interesting option -- they could compete with the Huffington Post et al. Online news is still based strongly on newspapers, so there's room for someone to shake up the format.
This all seems like a stretch, though. Yahoo's name has little value, and their current expertise isn't very helpful. All they bring to the table is more money than a startup, but it probably won't be enough to save them. Then again, that's what I said about Apple too.