Hitomi Kanzaki is in a very depressed mood. She only wants to sleep and fade away. Her misery summons Lord Folken who sends her to Gaea. The people of Gaea think she is the Wing Goddess, who can call upon the legendary Dragon Armor called Escaflowne. On Gaea, King Van, the sole survior of the White Dragon Clan, is also in a depressed state. Swearing an oath to get his revenge on the Black Dragon Clan that obliterated Van's kingdom, he lives by the sword. Now that the Wing Goddess has finally appeared, she posseses Gaea's world fate in her heart. Escaflowne will either lead Gaea to peace or total ruin.

(Source: ANN)

Haruka Nanase has reconciled with his rival Rin Matsuoka, and they have re-established their friendship, determined to race each other again. Now Haruka, along with Makoto Tachibana, Rei Ryuugazaki, and Nagisa Hazuki, prepare for their upcoming tournaments, determined to compete wholeheartedly and achieve victory as a team. At Samezuka Academy, Rin resolves to do the same. Further, the seniors near graduation, and Rin has decided his future plans. However, Haruka and Makoto remain uncertain, and they begin to feel the pressure of having to choose their own paths. [Written by MAL Rewrite]

Recap of the Free!: Dive to the Future TV series featuring new scenes.

The year is 2148. Two years after the end of the original Fafner in the Azure TV series, Tatsumiya Island and its surviving residents have returned to some semblance of recovery. However, things have become desperate for our hero, Kazuki; nearly blind now, and partially crippled from his battles with the Festum two years earlier, he clings to the promise his fallen friend Soushi made to him to return to the island and set things right again. Kazuki's hopes flare when a lifeform is detected within an unmanned submarine that comes floating into Tatsumiya Bay one night, but the person aboard isn't Soushi; it is a mysterious "boy" named Misao Kurusu who may not be entirely human, and who claims to have been sent by Sōshi. With Misao's arrival, hostilities break out anew between the Human Army and the Festum, and the Fafner pilots are thrown into the most desperate battle of their lives - this time, with the fate of TWO races riding on their shoulders. 

(Source: Wikipedia)