The clip is extremely short, so don't expect much in the way of spoilers. Basically, Dumbledore (Michael Gambon) uses the Pensieve to show Harry the first time he met Tom Riddle, who would become Lord Voldemort.
Almost more interesting is the strained pre-clip interaction between the movie's three leads. We don't know whether they were going for humor (and failing) or just ready to be done with the series.
Give the video a look:
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