The annotations for the Little Match Girl fairy tale are below. Sources have been cited in parenthetical references, but I have not linked them directly to their full citations which appear on the Little Match Girl Bibliography page. I have provided links back to the Annotated Little Match Girl to facilitate referencing between the notes and the tale.

1. Last evening of the year: New Year's Eve, as mentioned specifically later in the story. The Christmas and New Year holidays are known for great times of charitable giving. This story has become one of the most popular tales for inspiring charitable donations, especially during the Christmas holidays. It's also a reminder that this little girl, like so many others in poverty, needs help every day of the year, not just Christmas.
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2.  Slippers: The son of a cobbler, Andersen shows great interest in shoes and slippers in many of his tales, as well as feet such as in the Little Mermaid.
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3.  Nobody had bought anything of her the whole livelong day; no one had given her a single farthing: Begging was illegal during Andersen's time. The poor would make matches and sell them on the street as a front for their actual begging.
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4.  She crept along trembling with cold and hunger: Shivering is one of the early symptoms of hypothermia. It is muscle activity generated by the body to produce heat. As the body cools down further, shivering will stop.

You can read more about hypothermia, its symptoms and treatment at WebMD.com and NatureSkills.com.

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5.  In a corner formed by two houses, of which one advanced more than the other, she seated herself down and cowered together: Sitting down to rest in the cold is the worst decision to make when threatened with freezing to death, medically known as hypothermia. Movement and exercise helps the body retain heat. Sitting quickens the onset of hypothermia and consequent death.
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6.  From her father she would certainly get blows: Not only is the child cold and hungry, she is also abused at home, increasing the pathos and stark reality of the story.
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7.  Largest cracks were stopped up with straw and rags: Straw and rags were often used for insulation and building materials in the ill-made shelters of the poor.
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8. Oh! a match might afford her a world of comfort, if she only dared take a single one out of the bundle, draw it against the wall, and warm her fingers by it: The matches are her wares to be sold, not to be used by herself despite her misery. Surely using the matches without receiving money would cause another beating at home.
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9. The stove vanished: she had only the remains of the burnt-out match in her hand: Vision number one. This vision directly addresses the girl's coldness.

As the little girl begins to freeze, she experiences four visions. Some might consider all four to be hallucinations, since hallucinations are a common symptom of hypothermia. While Andesen probably considered the first three visions to be hallucinations, his religious beliefs insure his intention that the final vision of the grandmother be a real experience.
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10.  The goose hopped down from the dish, reeled about on the floor with knife and fork in its breast: Vision number two. This vision directly addresses the girl's hunger. Goose is a traditional meal served during the Christmas and New Year holidays, but one the matchgirl's family could ill afford.

The image of the goose dancing with knife and fork in its breast may be horrifying to some sensibilities but cartoonish to others. Andersen's intent is unclear.
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11. The most magnificent Christmas tree: Vision number three. While this vision does not address any of the girl's physcial needs, it reinforces the tale's Christian themes and foreshadows the girl's vision of her grandmother in heaven that follows. It also provides the device for seeing the shooting star in the sky.

You can read more about the history of the Christmas Tree, which was in use during Andersen's lifetime, on the Christmas Tree Farm Network and The Christmas Archives.

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12.  "Someone is just dead!": While the shooting star foreshadows her own death, it is debatable that this particular star represents the girl due to its timing in the story.
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13.  Her old grandmother, the only person who had loved her: Andersen also had a grandmother who doted on him, whom he remembered fondly in his memoirs and honors in this tale.
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14.  When a star falls, a soul ascends to God: A folklore superstition. A corollary superstition states that a shooting star represents a soul escaping purgatory.

A similar Creole superstition states: "Shooting-stars are souls escaping from purgatory: if you can make a good wish three times before the star disappears, the wish will be granted." NEW ORLEANS SUPERSTITIONS by Lafcadio Hearn

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15.  There stood the old grandmother, so bright and radiant, so mild, and with such an expression of love: The fourth and final vision.

Many near-death experiences around the world, regardless of religious belief, involve the visitation of dead loved-ones, usually family members and close friends.
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16.  Both flew in brightness and in joy so high, so very high, and then above was neither cold, nor hunger, nor anxiety--they were with God: Andersen's religious beliefs included a firm belief that the innocent enter God's presence at death where there is no more suffering.
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17.  Frozen to death on the last evening of the old year . . . No one had the slightest suspicion of what beautiful things she had seen; no one even dreamed of the splendor in which, with her grandmother she had entered on the joys of a new year: This is Andersen's version of a happy ending. The little girl is with God and her grandmother, never to suffer more in her worldly existence. Even being rescued from her plight and escaping death would not be as wonderful to him as the ending he chose.

Despite Andersen's obvious intentions, many translators and publishers of the tale have balked against this ending, occasionally offering a "happier" ending with the young girl being rescued by a family, to be fed and warmed on New Year's Eve with the implication that all would be well with her in the coming year.

Either ending serves another great purpose: reminding people to be charitable and help the poor during the holidays, and hopefully year round, to keep young children from suffering with poverty and death.
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