What is the first tier of raids in Mist of Pandaria?

According to Blizzard, the initial raid content is going to be split up into three mini-tiers, with Mogu'shan Vaults being the first of these tiers:

1. Mogu'shan Vaults

Open one week after launch for normal raiders, the main adversary is the Will of the Emperor, which is less of a boss than an event, as described by Ion Hazzikostas, lead encounter designer:

The core chamber of the Vaults contains an army of terracotta warriors that are built into recesses within the walls. If players look up, they’ll see these statue-filled niches stretching above them into the distance. When the players enter, the statues begin animating and attacking in huge waves, and the fight quickly turns into a free-for-all. There will be certain heavy-hitting statues that require tanking, and many of the other statues have special abilities to keep the non-tanks busy. It’s going to be a crazy fight that requires lots of crowd control.

The next two mini-tiers are reportedly the Heart of Fear and the Terrace of Endless Spring, which correspond to two parts of the same narrative:

2. Heart of Fear

Open four weeks after Mogu'shan Vaults for normal raiders, the main adversary is Grand Empress Shek'zeer, who:

has been possessed by the Sha of Fear

3. Terrace of Endless Spring

Open for normal raiders once they complete the Heart of Fear, the main adversary is the Sha of Fear, who:

has escaped the Heart of Fear once Grand Empress Shek'zeer was defeated.

Edit: Didn't see that the answer above also has the dates (not with numbers but with words) sorry for the repetition)

Adding this answer to add the exact dates of the releases of these raids (as they are not accessible right from the start):

September 25: MoP launches

October 2: Mogu'shan Vaults (normal) opens

October 7: Mogu'shan Vaults (LFR) opens, those who cleared normal Vaults can access heroic mode

October 30: Heart of Fear and Terrace of Endless Spring (normal) open, with Terrace only accessible by clearing Heart

November 6: Heart of Fear and Terrace of Endless Spring (LFR) open; queuing for Terrace requires clearing Heart. Those who cleared normal Heart can access heroic Heart, same for Terrace.

Source: http://us.battle.net/wow/en/forum/topic/6201711873?page=13#259

There are currently three raids that have been announced: Heart of Fear, Mogu'shan Vaults, and Terrace of Endless Spring. Currently, only Mogu'shan Vaults has been unveiled and opened for testing on the beta. The other two are highly subject to change before we know more. The Vaults will most likely be released similar to how they are on the beta.

Blizzard announced that the three raids will be released in stages, with Heart of Fear opening up four weeks after Mogu'shan Vaults, and Terrace of Endless Spring opened once players clear the Heart of Fear.

These descriptions are available on the beta in the dungeon journals. If you don't have access to the beta, they are also referenced and kept updated at wowpedia.

Mogu'shan Vaults

Description: The mogu, proud of their supremacy, kept lengthy records of their accomplishments within a great complex of vaults. Guarded by ferocious magical beings, these sacred chambers have remained silent since the mogu's departure.

Bosses

The Stone Guard - The first line of defense against those daring to enter the vaults is a stolid row of enchanted, bestial statues. Hard as granite and ceaseless in their vigil, the sentries of the Stone Guard present an insurmountable wall of flame, fangs, and claws.

Feng the Accursed - Long ago, Feng Shri was the Mogu'shan Vaults' caretaker, tasked with preserving the treasures kept within these shadowy halls. After years of faithful service, he was caught stealing from the shelves, although some say he was framed by a jealous underling and the mogu ruler punished him with a fatal curse. The doomed spirit of Feng Shri has wandered the vaults ever since, communing with the shades of past mogu heroes and warlords.

Gara'jal the Spiritbinder - Leader of the Zandalar trolls' assault on the vaults, Gara'jal is determined to crack open this trove of ancient mystery and bring back whatever arcane power and knowledge he can find. Gifted with dark talents and surrounded by a loyal cadre of Zandalar mystics, he has broken through the outer walls and will not rest until the vaults belong to him.

The Spirit Kings - Ancient records tell of these legendary rulers, powerful mogu who carved an empire out of the very rock of Pandaria. Their names still cause the lands to tremble: Zian of the Endless Shadow, Meng Sharpfang, Qiang Steelskin, and Sebotai Swiftfoot. Some say their spirits lurk in the vaults, lost in ghostly memories of battle and glory.

Elegon - Dedicated to the advancement of their empire, the mogu salvaged and repurposed titan technology to generate untold power in the depths of this ancient complex. Why these energies have been focused into the cold will of a celestial dragon is a mystery that lies at the very heart of the vaults.

Will of the Emperor - The core chamber of the vaults is protected by stone soldiers who have been motionless for centuries. They are row upon row of warriors, statues armed for a battle that never began. What treasures do they guard? And what is their tie to the titanic power buried with them here in the shadows?

Heart of Fear

Description: This is the seat of the Mantid dominion, and a place where the Queen of the Mantid currently resides, possessed by the Sha of Fear. It is located in a large, rotting tree structure in the center of the Dread Wastes.

Bosses

Imperial Vizier Zor'lok - Zor'lok shrieks his proclamations so they're heard throughout the sprawling mantid palace. He is the Voice of the Empress, and his words alone inspire the insectoid race's warriors to give their lives without question. Unwaveringly loyal, Zor'lok will stop at nothing to defend his beloved matriarch, regardless of the corruption within her.

Blade Lord Ta'yak - Ta'yak is known for his patience and intelligence. In battle, he is a master at discovering his opponent's weaknesses and awaiting the perfect opportunity to strike. Ta'yak's skill with a blade is unmatched, and he cherishes imparting his martial knowledge on young mantid warriors.

Wind Lord Mel'jarak - Wind Lord Mel'jarak commands the mantid's numerous aerial forces. Although he exudes arrogance, the cunning insectoid is fiercely protective of his soldiers and enjoys fighting at their side. Mel'jarak believes the mantid are superior to all other races, convinced that his kind cannot be defeated.

Garalon - It may be time to reconsider stepping on bugs. Don't make fun of this hulking behemoth's tiny wings; that'll just make him angry (Garalon is a massive Kunchong).

Amber-Shaper Unsok - Eager to please his empress, Un'sok has produced several innovative concoctions. Yet this brilliant young alchemist's proximity to the mantid queen has allowed the sha's negative energies to take root in his mind. Now, Un'sok's overwhelming fear of failure drives him to create increasingly deadlier weapons.

Grand Empress Shek'zeer - The ancient Klaxxi order has come to a mournful decision: the tainted grand empress Shek'zeer must be deposed. Traditionally, mantid rulers are displaced in their old age by a carefully chosen successor. However, Shek'zeer's intended replacement is still too young and weak to unseat her, leaving the Klaxxi with no choice but to kill the current empress. If action is not taken against her soon, all of Pandaria may crumble before the mantid's ravenous swarms.

Terrace of Endless Spring

Description: Straddling the mountain range between the Jade Forest and the Vale of Eternal Blossoms, the Terrace of Endless Spring has been a sacred refuge for millennia. Its peaceful fountains are said to have the power to heal and rejuvenate, but when the Sha of Fear attacked, many of the complex's guardians turned on each other in fits of terror.

Before a player can attempt to enter Terrace of Endless Spring, the Heart of Fear raid must be completed first. This will be a short four-boss raid.

Bosses

Protectors of the Endless - When the Sha of Fear invaded the Terrace of Endless Spring, three venerated jinyu protectors were corrupted, and they betrayed the other mortal sentinels, slaying them all. The twisted guardians have now turned their attention to any intruders who might interrupt the sha's attack on the area's last defenses.

Tsulong - Legends speak of a spiraling, golden serpent that can sometimes be seen high in the sky, basking in the sunlight above the clouds. The few who claim to have observed it themselves say the creature is fiercely protective of the terrace.

Lei Shi - For countless years, this friendly water spirit frolicked in the Fountains of Endless Spring with childlike wonder and glee. When fighting suddenly broke out in this peaceful place, Lei Shi saw the crystal-clear water turn cloudy and murky, and terror fell over her mind.

Sha of Fear - The Sha of Fear is the physical manifestation of terror in Pandaria. Imprisoned by the legendary pandaren emperor Shaohao long ago, the entity has been newly strengthened by rising conflict across the island. It should be noted that this entity is personally responsible for the corruption of the mantid swarm through Grand Empress Shek'zeer.