Mists of Pandaria will introduce Scenarios to give us instances similar to PVE Battlegrounds as well as staged, instanced group quests to revisit older content. These quests are designed for a few players and are intended to be short instances.
In order to enter a Scenario, players will queue in something similar to the Dungeon Finder, but will not have to choose a role -- hopefully making the queues very short. Scenarios are designed so that players won't have to designate a tank or healer and still be successful, much like when questing as a group normally.
Remember the days of Alterac Valley when the PVE elements were actually used and it wasn't just a PVP zerg? (I miss those days.) The Scenarios like PVE battlegrounds will be very much like Alterac Valley but without the PVP. The group of players will have staged objectives to complete in order to beat the scenario such as killing a number of enemies and capturing towers. This was designed for players who want to experience Battlegrounds but don't like PVP.
There will also be staged quests set in familiar locations, such as the Battle of Goldshire. Players and their groupmates will complete the objective of each stage until coming to the final boss. The example given was that the first stage might be to kill 25 kobolds, then you would rescue 4 children in the second stage and finally killing Goldtooth in the third. These will most likely be the replacement for group quests.
The rewards for completing Scenarios would include Valor points, much like the new daily quests. This continues Blizzard's goal of most gear being accessible to all players, regardless of playstyle.
Remember, all of this may change before launch.
The news is out -- we'll be playing Mists of Pandaria! Find out what's in store with an all-new talent system, peek over our shoulder at our Pandaren hands-on, and get ready to battle your companion pets against others. It's all here right at WoW Insider!