Draining in essence means: To cause something (usually liquid) to run out from somewhere.
In the case of this sentence, it means that someone takes energy from you leaving you depleted (depleted means used up or emptied out)
So when we talk about draining energy, it is as if you at night filled up your energy, and the interaction with someone is slowly, but surely, taking that energy from you and making you tired.
In psychology people can be energy givers or energy drainers.
I hope this answers your question.
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