Simply stated, "Method" acting is acting "real" by using experiences and impressions from the actor's own life to create the parallel experiences and impressions of the life of the character onstage. 

Lee Strasberg, considered by many to be the father of Method Acting,  described the results of using Method Acting by stating that "conventional" acting comes out to you, the audience, and "shows" you, and "demonstrates" to you. ["Method"] acting demands that you, the audience, go where it is going, so that you not simply understand what the character is experiencing, you also experience it.

Training in the fundamentals of Relaxation, Sense Memory, Concentration & Imagination, the Method actor begins the lifelong process of using himself to breathe life into the fiction of the play, as his inner awareness and artistic sense of truth develop with time and experience.

Method Acting as we know it today first became highly publicized when Marilyn Monroe made it known she was studying acting with Lee Strasberg.  This "announcement" drew attention from the Media, and soon the phrase caught on throughout the world.

The list of prominent actors who use the techniques, or "procedures" of Method Acting is too long to include at this site.  A few of the more notable past and present practitioners are Marlon Brando, James Dean, Al Pacino, Ellen Burstyn, Martin Landau, Dustin Hoffman, Shelley Winters, Harvey Keitel, Christopher Walken, Montgomery Clift, Lee J. Cobb, Lorraine Bracco, Robert De Niro, Robert Duvall, Sally Field, Jack Nicholson and Jane Fonda.