In Tennessee William's The Glass Menagerie, Jim asks Laura whether she has any interests. This is when she shows him her collection of glass animals, which she says Amanda refers to as a "glass menagerie."
As she explains what it is, she brings out one of the animal and trusts Jim enough to take good care of it. Jim asks what animal it is, and Laura tells him that it is a unicorn, and that it is also the one animal in the menagerie which means the most to her.
The conversation that follows is pretty much alludes to Laura's own personality:
JIM: Unicorns, aren't they extinct in the modern world?
LAURA: I know !
JIM: Poor little fellow, he must feel sort of lonesome.
This shows us that Laura identifies with the unicorn because she, too, is a person that is very unique in her naivete and innocence. She also seems to belong to an extinct class. Like the unicorn, she must feel quite lonely in a world with which she does not seem able to "catch up". By trusting the unicorn to Jim, she is basically trusting that she can open up to him and be herself.
When Laura gets more comfortable and Jim invites her to dance, they bump against the menagerie, the unicorn falls, and its horn is broken. This makes the unicorn turn into just a regular horse.
JIM: Aw aw aw- Is it broken?
LAURA: Now it is just like all the other horses.
JIM: It's lost its -
LAURA: Horn! It doesn't matter. Maybe it's a blessing in disguise.
Just like the unicorn is now "just like all the other horses", Laura (for the first time) feels just like all the other girls. She finally feels free and comfortable and, to boot, she has Jim O'Connor right in front of her. This must be the happiest moment in her life. This, too, is why she calls this moment "a blessing in disguise".