A Master Samurai is a samurai that has her samurai capacitity used to the fullest. The power of a Master Samurai is multiple times greater than that of a normal samurai. The samurai becomes a Master Samurai when she makes a pact with a general. In the anime, the generals are men and Master Samurai are women.
A Master Samurai can go into Master Samurai mode whenever she wants by saying her life motto. In Master Samurai mode she gets new clothes, weapons, and abilities (like controling certain elements). Their speed and strength are also multiple times bigger than when in normal mode.
The personality of a Master Samurai in Master Samurai mode is usually the same as in normal mode. The only exception is Jūbei Yagyū whose personality changes drasticaly because of an unknown reason.
The power of a Master Samurai is multiple times bigger than a normal samurai's. In Master Samurai mode, she gets the ability to control certain elements like ice, fire, lightning, or wind. Her speed and strength are also far greater than when in normal mode.