Refurbs from Apple are almost entirely brand new, except for the "guts." New casing, screen, battery, and anything that was wrong with the original unit is fixed.
You will not be able to tell the difference. The "refreshed" iphones that you sometimes see are ones that have just been cleaned up and re-sold. That is not the case with Apple official refurbs.
Current arsenal: iPhone 5 16GB / iPad 2 WIFI 16GB / Apple TV 2 / Slingbox Solo / Acer Aspire Z5610 touchscreen all-in-one / Acer Aspire netbook
Fallen soldiers: iPhone 4S 16GB / iPhone 4 16GB / iPhone 3G 8GB / BlackBerry Pearl 8100 / Motorola L6 SLVR / Nokia 5190, 3390, 8390, 3220 / Ericsson T18z / Mitsubishi G310 / Motorola C333 / Sony Ericsson T237