I was also ignorant about this so I googled. It said it means "Thanks for Asking" or "The fucking article". The second meaning sounded correct but I found it weird.
"The fine article" also sounds weird to me.
"The fine article" also sounds weird to me.
For usages see https://hn.algolia.com/?query=TFA&sort=byDate&type=comment
I've given up on trying to learn them and just take a stab based on context