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What does cache time mean?

It's the number of seconds before the content will be requested again. You can set this to be 0 or -1 to not use the caching system. If you edit any of the widgets in the widget admin panel, the cache is cleared.

My widget doesn't display any stories

This could be for many reasons. First possibilty, you incorrectly entered your Google Reader ID. Next, your host might not support filegetcontents or curl. Try changing the use option to curl in the widget admin panel. You could try using some sort of fsockopen if neither curl nor filegetcontents work. If your host doesn't support outside requests, this widget will not work for you.