I love reading fashion magazines and occasionally come across the word atelier. What is that?

Atelier is a French word that means studio or workshop, especially one that's used by an artist. Fashion designers also have ateliers.

In The Awakening, Edna Pontellier's father comes for a visit:

Edna and her father looked very distinguished together, and excited a good deal of notice during their perambulations. Upon his arrival she began by introducing him to her atelier and making a sketch of him. He took the whole matter very seriously.