The various styles of acting have been developed throughout the history of the theater, from the classical era in Greece, to the modern day of multimedia acting, incorporating the stage, film screen and television. In the modern era, an acting teacher named Constantin Stanislavski developed an acting style that uses the personal experiences and emotions of the individual actor to create a convincing performance. Later, this became extended by the Actor's Studio of New York City into "method acting."
Stage vs. Film
The technical style of acting was developed for the stage, and comes from the long formal history of stage acting, related to the live performance of music and dance. It's designed to be "read" even by audience members who are distant from the action and is highly formal. The "method" school, also called "subjective" acting, conforms directly to the concerns of film acting, which can be much more subtle and personal, due to the "up close" nature of film.
Identification
The method actor uses personal identification and internalization of the character he or she is portraying to better discover the motivation behind that character's actions and mindset. In finding recognizable and human traits, the method actor also wants the audience member to identify with the character.
Conveyance
The technical actor conceptualizes the character he or she is portraying as a conveyance, not necessarily a naturalistic or realistic depiction of a person you might encounter in life. This is reflected by the difference between "objective" versus "subjective" acting styles in which physical expression and projection of a character is more important than introspection and "small" acting.
Instinct and Improvisation
One area where method acting has a distinct advantage over formal, technical acting, is that the emphasis on internalizing character and motivation ultimately allows for improvisational acting. In more intimate theatre settings, on film and with comedy, improvisation creates spontaneous acting that's truly reactive to the other participants.