Will you be able to run any program?

Technically, any Web-based application will work, so long as it's able to operate in a standards-compliant browser. Even will run on a Chrome OS computer -- in fact, it's the software's default program for opening files such as Excel documents.

Does that mean you couldn't install your own browser, like Firefox?

More or less. Chrome is the default browser in the Chrome OS, and you can't install software onto a Chrome OS system. The only way around it would be if a developer such as Mozilla were to take Google's open source code, create its own version of the Chrome operating system, and then sell its own Chrome OS devices with the Firefox browser built in.

What about Android apps -- can you run those?