When people in Japan see "FF," they immediately think Final Fantasy. And for good reason! For decades, "FF" has been shorthand for the iconic role-playing game series. But recently, Twitter users have been using "FF" as a polite way to reply to others.
As GetNews reports recently, "FF" refers to "Follow" and "Follower." It is used the in the expression, "FF gai kara shitsurei shimasu" (FF外から失礼します), which basically means, "I don't follow you and you don't follow me, but please excuse me."
This is used when you want to reply to a tweet from someone you don't follow and who doesn't follow you. It's typically used during right before making your initial @ reply. Since Twitter allows users to re-tweet others, sometimes people might want to comment on tweets that show up in their timeline. By writing "FF gai kara shitsurei shimasu" they can do that in a polite way.
According to Keyword Note, "FF gai" started to appear on Twitter circa 2009 when users would comment on, for example, strange or random replies they got from others they didn't follow or who didn't follow them.
By around 2011, Keyword Note adds, it started to become more and more common for Twitter users to write "FF gai kara shitsurei shimasu" when intruding on others.
It makes sense in the context of Japanese manners, especially because the concept of inside the group and outside of it is strong culturally. Also, there are basic manners about imposing on others.
For example, when you visit someone's home, you say, "ojama shimasu" (お邪魔します) or "Sorry to disturb you." This is because you are entering another person's space, and excusing yourself for that imposition. On Twitter, this slang "FF gai kara shitsurei shimasu" works in a similar way. You're interrupting from the outside, and are excusing yourself for that.
— はりーシ（スカちゃんLoL動画投稿） (@Halli_4) February 25, 2016
Of course, the best place to use "FF gai kara shitsurei shimasu" is when you don't follow the official Final Fantasy account, but still want to make @ replies.
— NOBEL (@NOBEL827) December 12, 2016
Or when making cute Square Enix themed fan art.