Oscar Wilde uses his short story "The Nightingale and the Rose" to satirize Romanticism. Literature of the Romantic period focused on the individual and placed value in intense emotions above rational thought. In his satire, the color red of the rose has several symbolic meanings.
First, the color red symbolizes passion and romance, just as it typically symbolizes such emotions. We can tell red is symbolizing passion and romance since the story opens with the young Student bemoaning the fact he has "no red rose" in his garden. Since he has no red rose, he will not be able to dance with the girl he is in love with who promised to dance with him if he brought her a bouquet of red roses.
Second, the color red symbolizes mortality. When the Nightingale falls in love with the Student, thinking he is a true lover, she decides to do what she can to help him. She flies to every rose bush in the garden asking for a red rose, but none are able to provide her with with one, not even the red Rose-Tree, who has been damaged by a harsh winter's storm. The Tree says it can help her if she pierces her heart with a thorn, all night long, while singing. Doing so does indeed produce a red rose, yet it also kills the Nightingale. Since the Nightingale colored a rose with her own blood, we can see how the color red of the rose also symbolizes mortality.
Finally, it can be seen that the color red of the rose symbolizes anger or other intense, negative emotions. When the Student brings the red rose to the girl he loves, she rejects it, saying it would not go with her dress and that the Chamberlain's nephew has given her real jewels to wear. In his anger, the Student throws the rose into the street. Hence, in this moment, we see that the color red is also symbolizing his anger and even his blindness and foolishness that were a result of his passion.