It's a reference to Proust's Remembrance of Things Past, wherein he famously recounted how, upon eating a "dispiriting" madeline as an adult, he was abruptly and involuntarily taken back to the emotions of childhood, when he and an aunt shared madelines every Sunday. Since then, it's shorthand for "something that emotionally transports us back to happier times," more or less.

I think it's "one that evokes a memory": http://www.merriam-webster.com/dictionary/madeleine

That seems to be how it's used in the article and some of the comments here:

"Crimea was the ideal site for this post-Soviet reunion, since it was the place where so many children, now adults, had spent their happy summer vacations, flocking there from all over the Soviet Union. For post-Soviet people, Crimea was a gigantic madeleine."

I see others have beat me to a response. m-w also has a paragraph about it:

"The madeleine is said to have been named after a 19th-century French cook named Madeleine Paumier, but it was the French author Marcel Proust who immortalized the pastry in his 1913 book Swann's Way, the first volume of his seven-part novel Remembrance of Things Past. In that work, a taste of tea-soaked cake evokes a surge of memory and nostalgia. As more and more readers chewed on the profound mnemonic power attributed to a mere morsel of cake, the word madeleine itself became a designation for anything that evokes a memory."

I had never heard of it either.

>since it was the place where so many children, now adults, had spent their happy summer vacations, flocking there from all over the Soviet Union.

yes, Russian climate makes you yearn for hot climate vacation near sea and giving the Iron Curtain there weren't much options. These days Russians go en mass to Mediterranean : Turkey, Egypt, Greece, Chernogorya, Italy, Spain. Despite all the propaganda they aren't going to Crimea. As joke has it these days "it is so quiet on Crimea beaches that one can hear Russian tourists having drink party ("buhayuschih") on Egypt beaches"

This is also the reason that you sometimes find Madeleines flavored with earl gray tea. It's something of a literary joke about Proust, who helped make the cookies famous.

Technically, they are small cakes, not cookies.

I wasn't familiar with the term, but Wiktionary has some good hints:

n. A small gateau or sponge cake, often shaped like an elongated scallop shell.

n. Something which brings back a memory; a source of nostalgia or evocative memories (used with reference to its function in Marcel Proust's In Search of Lost Time).

It's a reference to Proust's "Remembrance of Things Past." The taste brings forth memories involuntarily.