You got the lights on in the afternoon
And the nights are drawn out long
The girl described in this song is an ex-lover of the narrator's. The relationship seems to have appeared out of nothing, gotten too serious too soon, and then faded.
These opening lines depict the initial, sexually-focused nature of the relationship. Putting the lights on in the afternoon is an attempt to make it seem later in the day early - she longs to go to bed (with him).
Also, the afternoon (or the day after) can bring regret in what you've done the night before. This means it could be a reference to Arctic Monkeys' early rocker The View From The Afternoon.