From Yoast:
I've seen it happen so often. People have a great blog, and at some point, they decide they need a new look and feel. They then decide to either buy one or use one of the free themes available at wordpress.org. There's a couple of things they'll look at, usually in the order: layout / look and feel, usability and optionally, room for advertising.
If the theme meets their needs in all two or three of these points, they download it and start installing it. If that's what you do too, this theme checklist is for you!
A theme has quite a few things it has to take care of, and a lot of themes out there don't take care of all of these. This is a checklist that should help you prevent getting into trouble when you start using a new theme.
If you're thinking of installing a theme, open up the directory that your supposed to upload, and check the following: