The entire collection of glass animals represents much throughout the play.  Williams might be attempting to make a statement that contrasts how reality should be as opposed to what is.  Laura's comfort with her glass animals, curating and being their caretaker is something that brings her happiness.  To a great extent, it allows her to enter a world where construction is what can or should be as opposed to the world in which she lives that represents a rather deadening representation of what is.  The unicorn highlights such significance because within the menagerie, it holds distinction, separation from all else.  Yet, when its horn breaks, standing with Jim, Laura remarks that it is not as "freakish" and it is "normal."  It is a critical moment because at that moment, when confronted with the hopes of being loved by another, Laura wishes that she, herself, could be more "normal," like Jim apparently is.  She wishes herself not to be so "freakish," so that she can find someone to love and not be so confined by her loneliness.  In this light, Laura's plight and the Unicorn are similar in that both confront the challenges of being different.  The symbolic difference is that the Unicorn's predicament is easily resolved with one break. Laura will not be as fortunate because she will always be looked at different.  Yet, Laura recognizes this and understands that this is going to have to serve as a part of her identity.  Given how the "normal" people behave such as Amanda's deception, Tom's misery, and Jim's ambivalence, Laura's blowing out the candles might serve as a point of commencement on this journey towards an embrace of self.  Her giving the unicorn to Jim could also reflect this, as she recognizes that he might need more support in order to be less "freakish" given his appearance of "having it all."