They probably mean plugged in to allow the internal components to reach--and then stabilize--at their optimum operating temperature.
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I found that mine (Gold Reflex) required more than just leaving it on for 72 hours. Mine gradually and continually sounded better after listening for about 3 weeks.
I also tried speeding up the burn-in process by hooking up my CD player to the phono stage and playing Granite Audio's phono burn-in CD.