From Diablo Wiki
MP10 refers to playing Diablo III with the Monster Power level set to the maximum value of 10. This setting greatly increases the monster hit points, but also boosts experience gain, Magic Find, Gold Find, and guarantees that the Keywardens will drop keys and the uber bosses will drop demonic organs, as part of the Infernal Machine event.
MP10 is also a popular play mode for players who want to level up quickly, either by playing alone for greater challenge, or with twinks and the assistance of a friend. It's easily possible to rush a new character from level 1 up to 60 in just a few hours, with teamwork and Monster Power 10.
Monster Power Settings
Infographics from Blizzard show how the game difficulty and reward scales up with each level of Monster Power. The values for Normal/Nightmare/Hell:
Monster Power on Inferno varies considerably from the earlier difficulty levels, with monster hit points and damage scaling up much higher. Note that the drop rates for the keys and demonic organs required for the Infernal Machine also receive considerable increases with each level of Monster Power.
With the introduction of this optional difficulty slider, many players found fun in playing a brand new character from level 1, on Monster Power 10. This can be done with twinks and Auction House access to accelerate the process, or in a more purist style, such as Live off the Land for greater challenge.