An acronym meaning "Ta ta for now."
Though popularized by Internet chat room slang, the initials themselves date back to World War II, when British comedian Tommy Handley hosted It's That Man Again! on the BBC. In a war filled with catchphrases and acronyms, the show's name was shortened to ITMA, and as part of a combined joke on the rise of war acronyms, radio acronyms, the snappy staccato humor of the time, and the cutesy nature of letter valediction ("SWAK", "XOXO"), "TTFN" became a minor British catchphrase.
It left prominence in the 1950s, was revived briefly by Valley Girls and Winnie the Pooh's Tigger, but has been brought back into full force by the preponderance of Internet shorthand in the past 10 years.