Tom is stuck in a life he hates. His father has left--a phone man who "fell in love with long distance." Tom is left to stay and support his mother and his "crippled" sisiter.
Laura is an odd little creature who is best represented by the unicorn in her glass menagerie. She can't do what other girls do because she sees herself as a freak or an oddity; we know this is probably not as true as she thinks,though, because Jim (an outsider) tells us he barely noticed her limp clear back in high school.
When Jim, her one and only gentleman caller, kisses Laura and the unicorn loses its horn--thereby becoming a horse, something much more "normal"--we have some hope for her future. Perhaps she can re-connect to the world somehow. Then Tom leaves, and Laura's future is left unrevealed and unresolved.
Tom, as you remember, is a poet. So, when Tom tells Laura, from a distant time and place, to blow her candles out, it's clearly a metaphor (picture of something more). He sees her in his memory and makes this observation:
"Oh, Laura, Laura, I tried to leave you behind me, but I am more faithful than I intended to be! I reach for a cigarette, I cross the street, I run into the movies or a bar, I buy a drink, I speak to the nearest stranger - anything that can blow your candles out!"
The candles are clearly connected to memory. Despite his best efforts, Tom has not been able to forget what he left behind--probably out of both guilt and shame at having deserted his family and at becoming the one thing he never wanted to become...his father.
He may be asking her to finally let him rest, memory-free--and therefore guilt-free. He may be once again pointing Laura out as the oddity, for she is still using candles when "nowadays the world is lit by lightning." Of course, it may be both or something else altogether.
In any case, Tom's request that Laura blow her candles out is probably more about him and his rather gritty future than anything about Laura.