The key word in regards to a third-person narrator, especially in Desiree's Baby, is the word "limited" or "omniscient." In this case, our third-person narrator is definitely "limited" and we can tell, as readers, because we cannot tell what other characters are thinking or feeling (especially in regards to Desiree and Armand).
We are limited by our narrator by what the narrator knows about Desiree. As readers, we are told that Desiree grew up with a particular nature:
The girl grew to be beautiful and gentle, affectionate and sincere.
We assume that she will remain so and continue to be loyal as well. As readers, we don't understand originally why the plantation changes after Desiree has the baby. Desiree doesn't understand either:
[There was] an air of mystery among the blacks; unexpected visits from far-off neighbors who would hardly account for their coming ... an awful change in her husband's manner.
Desiree eventually become miserable, especially when her husband tells her that a child that is not all white could only be her own fault. Desiree is loved and accepted by her adopted birth family; therefore, they make it clear that Desiree could come home with the baby. We are surprised by what happens next (and it is all because of the third person, limited narrator):
Desiree walks across the field and into the bayou. She and her child are never seen again.
It is a similar case with Armand in that the narrator isn't sure of the reasoning behind his actions. Originally, Armand seems to have the exact opposite nature of Desiree: unfeeling and fairly ruthless. The birth of the child changes him, that is, until the gossip starts about the child's lineage. When he is at home (which isn't often), he reverts to his old personality according to our narrator:
He absented himself from home; and when there, avoided her presence and that of her child, without excuse. And the very spirit of Satan seemed suddenly to take hold of him in his dealings with the slaves.
At this point, we know nothing about Armand's heritage, and assume he is from the prominent, white, Louisiana family that he is born from. The limited narrator takes us along on that ride. That is what makes the final statement at the end (the one revealing Armand's true nature and his own revelation) so shocking:
Our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery.
Through a letter from his mother to his father, then, Armand finally learns the truth: he is half black.
In conclusion, this narrator that is third-person and limited, gives the author a perfect opportunity to surprise readers when Desiree disappears into the bayou and when Armand finds the letter that reveals his African-American heritage. Chopin proves her writing ability as her readers (as well as her narrator) gasp in surprise at the amazing revelations of her characters.
The employment of a third-person narrator rather than an omniscient narrator limits what the reader knows about the inner thoughts of characters. Therefore, since this is the case, the ending of "Desiree's Baby" is more shocking to the reader; for, from the point of view of the narrator, Desiree has seemed of sanguine temperament: "The girl grew to be beautiful and gentle, affectionate and sincere..."
The feelings expressed in the narrative seem to be outside Desiree. For instance, after the baby is born and Madame Valmonde visits, she examines the baby in the light of the window, then says slowly, "Yes, the child has grown, has changed." Later, Desiree wakens one day and senses that
...there was something in the air menacing her peace....an air of mystery among the blacks; unexpected visits from far-off neighbors who would hardly account for their coming...an awful change in her husband's manner....
Thus, it is only outside forces that indicate possible conflict; the reader knows not what thoughts Desiree harbors. Thus, she seems but a victim of a surprising and cruel fate when Armaud condemns her as being responsible for the child's race that is not white. Furthermore, her meager words, "Shall I go, Armand," and her fatalistic action in her departure are completely unexpected by the reader, greatly adding to the impact of the ending.
A third-person narrator is like an eyewitness to the events of the story, telling the reader what he/she wants us to know. We may only be allowed to know what one character is thinking and feeling, and that is third-person limited. Third-person omniscient is where we get to see what most or all of the characters are thinking and feeling. A third-person narrator is also usually more reliable than a first-person narrator because he/she is not involved in the story itself.
By using a third-person narrator, we don't get to see what all of the characters are thinking or feeling. If we did, we might be able to know what Armand is thinking and feeling. If we could see inside his head, we would know what a scoundrel he is for getting rid of Desiree and their baby. We would also know why Desiree chooses to die with her baby instead of going home to the family that loves her. Because Desiree doesn't tell the story, we don't know what she's thinking. We have to infer certain things about why the characters do what they do.