The truth is that there are numerous layers to this particular song; several have been mentioned already.
First, Mimi is a heroin user. Heroin is typically cooked in a spoon over an open flame - a candle, for instance. So the top layer, literal, and obvious meaning of the song is that Mimi is looking for a light for her candle so that she can do her drugs.
However, watching the scene again you'll find that this can't account for all of it, because before entering we can see Mimi standing outside Roger and Mark's flat (during One Song Glory), and her candle is lit. She blows it out intentionally.
Why? She finds Roger attractive and is looking for a reason to introduce herself for companionship. So in this case, "light my candle" refers to Mimi's search for love.
On a more blunt level, the theme of many of Mimi's lyrics here are sexual in nature, so "light my candle" could also refer to Mimi looking for a sex partner - in this case, "light my candle" would be to have an orgasm.
From Roger's perspective, it seems like his heart has been somewhat "frozen" of love since the loss of April. Lighting a candle would allow that to be thawed out, so despite his awkwardness, Roger is looking for someone to be with as well.
And unknown to Mimi, Roger was a former heroin-user as well; to him, the candle symbolizes his addiction, which he has "blown out" - so his hesitation toward the end of the song to give Mimi her stash back is an indication that he worries that being with her might relight the candle of his own addiction.
The truth is that there are numerous layers to this particular song; several have been mentioned already.
First, Mimi is a heroin user. Heroin is typically cooked in a spoon over an open flame - a candle, for instance. So the top layer, literal, and obvious meaning of the song is that Mimi is looking for a light for her candle so that she can do her drugs.
However, watching the scene again you'll find that this can't account for all of it, because before entering we can see Mimi standing outside Roger and Mark's flat (during One Song Glory), and her candle is lit. She blows it out intentionally.
Why? She finds Roger attractive and is looking for a reason to introduce herself for companionship. So in this case, "light my candle" refers to Mimi's search for love.
On a more blunt level, the theme of many of Mimi's lyrics here are sexual in nature, so "light my candle" could also refer to Mimi looking for a sex partner - in this case, "light my candle" would be to have an orgasm.
From Roger's perspective, it seems like his heart has been somewhat "frozen" of love since the loss of April. Lighting a candle would allow that to be thawed out, so despite his awkwardness, Roger is looking for someone to be with as well.
And unknown to Mimi, Roger was a former heroin-user as well; to him, the candle symbolizes his addiction, which he has "blown out" - so his hesitation toward the end of the song to give Mimi her stash back is an indication that he worries that being with her might relight the candle of his own addiction.