Nameplates in Diablo III refer to the visible health bar at the top of the screen of the selected target. When Diablo III was announced, there was a lengthy gameplay movie shown where the nameplates would hover roughly around where the cursor was. One nameplate would be visible at the time. Due to the screen being as busy as it is, Blizzard decided to make the change to have the nameplate at the top of the screen, in a central position, to help alleviate "noise". Nameplates for bosses are always visible, presumably while they're in range.
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Siege breaker nameplate in 2008.