To light a fire again, or figuratively to bring back or revive a feeling, relationship, or interest that had faded or been lost.
From 're-' (again) plus 'kindle' (to light or ignite). The metaphorical sense developed naturally as fires and emotions both need fuel to survive.
Rekindle is one of those perfect metaphors that works because fire and emotion behave so similarly—both need oxygen to survive, both need fuel, and both can die down to embers before reigniting.
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