Classic fashion brand Burberry goes digital

Cohen says iconic luxury fashion brands have the story to attract consumers, but the challenge is finding the right means of communicating it in the digital world. "They have to turn the store into a story and the story into a site," Cohen said.

The Burberry website offers 10 times more online than what the company has in stores "because we say that is 'the world's store,'" Ahrendts says.

Mobile commerce gives customers instant access to products they aspire to own. "To me, the key is that even the luxury brands have to learn, have to evolve," Cohen says. "Without evolution the luxury brands will be overtaken by more progressive, up and coming luxury brands. Luxury has to worry about keeping their brand alive."

Burberry is interacting directly with consumers in the digital sphere too, launching projects like artofthetrench.com. The website invites users to upload pictures of themselves wearing Burberry trenchcoats, which have been made by the label since World War I. The result is a collage from around the world.

Burberry.com also features Burberry Bespoke, which lets users customize their own trench, down to buttons and belts.

Ahrendts wants Burberry online and Burberry offline to be seamless for customers. But it's not without challenges in a digital world where fashion buyers can become overwhelmed with emails, tweets and others messages.

"How do we keep the brand so cool and so pure and so relevant so it cuts through that clutter?" she wonders — then answering her own question. "But by the same token how do we keep the marketing and the communication much more customized and personalized."