In an allusion to the famous Renaissance artist, the March sisters call Amy "Raphael" because she likes to draw and paint. 

"Little Raphael," as her sisters called her, had a decided talent for drawing, and was never so happy as when copying flowers, designing fairies, or illustrating stories with queer specimens of art. Her teachers complained that instead of doing her sums she covered her slate with animals, the blank pages of her atlas were used to copy maps on, and caricatures of the most ludicrous description came fluttering out of all her books at unlucky moments.

The nickname is a compliment; Amy has great artistic talent and takes pleasure in being creative. An allusion to a lofty Renaissance artist heightens this comparison; the girls do not merely call her an artist but rather choose a specific one. Raphael's work was grand and colorful, just like Amy's drawings and Alcott's prose. Though the March sisters don't mean that Amy will necessarily become a famous artistic master like him—there's an element of gentle exaggeration here—they do acknowledge that art is an animating joy in Amy's life, which they admire.

This allusion also demonstrates the girls' fairly high level of education. Although the Marches do not have much money, they have many other valuable resources that enrich their lives, such as the ability to study and enjoy art, albeit in a limited way.