In the final scene of "The Glass Menagerie", Tom's monologue syncronizes directorily with Laura blowing out the candles of the candelabra.  It was the candelabra that Amanda had given Jim (the gentleman caller) to take and go talk to Laura who felt sick and left the room when she discovered that the gentleman caller was the boy she had a crush on in high school.

Tom leaves the house forever after he is berated by Amanda for bringing home a gentleman caller for Laura who (unbeknownst to Tom) was already engaged.  Tom leaves St. Louis and "descended the steps of this fire escape for the last time and followed from then on, in my father's footsteps, attempting to find in motion what was lost in space. . .Perhaps it was a familiar bit of music.  Perhaps it was only a piece of transparent glass. . .  (referring to Laura's glass menagerie). Perhaps I am walking along a street at night, in some strange city, before I have found companions.  I pass the lighted window of a shop where perfume is sold.  The window is filled with pieces of colored glass, tiny transparnet bottles in delicate colors, like bits of a shattered rainbow. Then all at once my sister touches my shoulder.  I turn around and look into her eyes.  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 following passage synchronizes with Laura blowing out the candles) . . . For nowadays the world is lit by lightning!  Blow out your candles, Laura---and so goodbye. . . "  (She blows the candles out.) 

Tom is troubled by how he deserted Laura.  He tried to help her and his mother, but he could not live with them any longer--the guilt is overwhelming and he finds no peace.  He wants the interminable reminder of what he has done to end. . .  and thus asks Laura to forgive him and to forget about him.  This is the symbolism in the passage of asking her to blow out the candles.  Laura and Amanda are destined to continue living their lives with little income and no husband to take care of Laura.  Tom is asking her forgiveness and she grants his request by blowing out the candles.

Note:  In real life, Tennessee Williams' sister's bedroom was next to an alley where she could hear cats fighting and screaming at night as she went to sleep.  So Tennessee painted her room white and brought home little pieces of colored glass for her to collect in order to brighten her room as well as her spirits.

Tom wingfield, a poet with a job in a warehouse, acts as narrator of The Glass Menagerie. As such, he explains that it is a memory play, and in memory everything seems to happen to music, so there is a fiddle playing.  In addition, the subdued lighting in the play, especially in the last scenes, suggest romanticism and intimacy.  When Jim informs Laura that he accepted the invitation to dinner with Tom he had no idea about her, the stage directions read,

The holy candles in the altar of Laura's face have been snuffed out.  There is a look of almost infinite desolation.

The intimacy is broken and Laura is left hopeless.  Likewise, when Tom tells Laura to "blow out your candles,Laura--and so goodbye," he, too, breaks the intimacy that they once had, rupturing the past.  When Laura does blow out the candles, Tom takes his release from her as the play ends.  Tom has used this art as an attempt to erase his pain, much as the playwright, Tennessee Williams, himself used art.  Unfortunately for Laura, this break by Tom leaves her bereft in a hopeless existence.

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.