This is not meant to discourage anyone from posting, but you may be interested in this thread from a few months ago. I'll quote my own answer from that thread here:

First, technique – Film acting at least partially takes place on the editing room. The audience will tend to impress emotions and thoughts on actors depending on the visual context of the shot; this was documented as early as the 1910s, when Russian film-makers, critics and theorists such as Lev Kuleshov started experimenting with montage to construct meaning in film. The same shot of an actor's face would be interpreted differently by the audience depending on what it was cut with – the same expression, alongside a bowl of soup, a casket, or a woman, would indicate hunger, sadness, or lust respectively.

These ideas eventually seeped into film-making all over the world. In Hollywood, European vanguard ideas about film were mainly introduced in two ‘waves,’ the first one being mainly German expatriates who came to America to work on film after the vibrant, experimental vanguard cinema of the Weimar republic collapsed. The second were American film-makers who came into the industry in the sixties and seventies, who had a very different perspective and background from their predecessors; unlike the old guard, they had not only grown up with movies but studied film in an university environment, and were very acquainted with the work of European cinema throughout history as well as the writings of film theorists of the era.

The use of montage and photography to communicate the internal states of characters on screen naturally lends itself to a more subdued style of acting, as the actor is doing less of the work of communicating the character's processes to the audience. If you look at a modern-day prestige drama, especially something on television such as (Say) Mad Men, the so-called ‘Kuleshov Effect’ is doing a lot of the heavy lifting of exposing the characters' emotions to the audience.

In early film, the absence of sound and the preponderance of full-body shots made ‘acting with your whole body’ the norm, and the style of acting that goes with that stuck around after the development of close-up shots (Gradually over the 1910s and 20s) and synchronised audio (Late 1920s and 30s).

It is also true, of course, that the experiences of film-makers outside Hollywood shows that there's no natural or inherent connection between silent film and a ‘histrionic’ style of acting; I feel like the acting style in early Hollywood film is better explained by cultural factors rather than technical limitations of the medium. But speaking of which...

Cultural factors: The very first generation of actors in Hollywood came largely from vaudeville and other forms of popular theatre. They would have been most acquainted with broad comedy and melodrama, genres that aren't exactly known for their restrained performances; and since early narrative film targeted the same audience as vaudeville, those actors, and the style and training they had, were a good fit.

As cinema struggled to gain cultural validation in America and sell itself to middle- and upper-class audiences, film actors increasingly came from a more classical theatre background. This is the mannered, representational performances you see in Classic Hollywood Cinema. It's associated with the (artificial) ‘midatlantic’ English dialect, clarity of enunciation, and a more formal (As in formalism, not formality) approach to acting.

Meanwhile, of course, a cultural revolution was taking place in theatre; the Stanislavski method, developed by Russian theatre actor and director Constantin Stanislavski over the course of the 1910s and 20s. The Method, often called ‘method acting’ does (For some practitioners) involve staying in character for long periods of time, but originally it focused on the idea of the ‘emotional memory,’ using the actor's real memories of his life experiences to build a character. Later, Stanislavski would focus on the study and reproduction of physical actions. This method would eventually not only be brought to America (It is most famously taught at the Actors Studio in New York) but also largely supplant the more mannered classical style. This shift can be seen in later Classical films, starting A Streetcar Named Desire – Directed by Actors Studio founder Elia Kazan. By the time the classical era ended, the method had cemented itself in Hollywood.