PDD1 is "Production Development Division 1".
Basically the main team that works on mainline Final Fantasy and Kingdom Hearts titles.
A lot of people think there's a "Kingdom Hearts team" but it doesn't really work that way. PDD1 jumps between mainline franchises. Fun fact: The original team that made Kingdom Hearts was 1/2 of the Final Fantasy X team while the other half made Final Fantasy X-2 (which required fewer staff).
This is how Square-Enix is organized to the best of my knowledge:
PDD / Description / Head of Division / Recent or Notable Franchises & Games
PDD1: Flagship - Yoshinori Kitase (mainline Final Fantasy, mainline Kingdom Hearts)
PDD2: Spinoffs & IPs - Akitoshi Kawazu (The Last Remnant, SaGa, Crystal Chronicles)
PDD3: MMORPGs - Hiromichi Tanaka (Final Fantasy XI, Final Fantasy XIV)
PDD4: Quest - Yasumi Matsuno (Ivalice Alliance and most of FFXII, Tactics Ogre)
PDD5: Osaka - Yusuke Hirata (Kingdom Hearts Birth by Sleep, Musashi: Samurai Legend)
PDD6: Inactive/defunct - Toshiro Tsuchida (Front Mission)
PDD7: Ports and Remakes - Takashi Tokita (FFIV DS & FFIV TCC, FF: 4 Heroes of Light)
PDD8: Inactive/defunct - Koichi Ishii (Mana series)
PDD9: Enix / Dragon Quest - Yuu Miyake (Dragon Quest series)
PDD10: Contractees - Yosuke Saito (This division handles outside contractees like h.a.n.d which they supervise to make games like Days and other IPs. Nier from former studio cavia would have fallen under this.)
Other development divisions abroad (mostly Eidos):
Square-Enix LA (Project Dropship, also I think their studio was axed recently. :I)
Crystal Dynamics (Tomb Raider)
IO Interactive (Hitman, Kane & Lynch)
Eidos Montréal (Deus Ex: Human Revolution)
Beautiful Game Studios (Championship Manager)
Eidos Shanghai (middleware)