What does this message mean - "Files on the phone are newer"?

This happens when you update a feed, then later when another update occurs, the newly fetched feed is older than the original.

This has happened for me when I update a feed on wifi, then later update over the cell network. Sometimes data is cached (my theory at least) on the carriers proxy servers so you don't get the new version of the feed. You can confirm this is happening to you by opening the feed in the Android browser and you'll probably be seeing the old version of the feed.