“The Method” is a style of acting that was popularized by the Russian actor Konstantin Stanislavski. It was made much more popular in the United States by Lee Strasborg.
The basic idea of The Method is that the actor should believe they are the character that they’re playing. They should “lose themselves in the role” by linking the character’s experience to their own experiences. Thus, the emotion they experience on screen or stage will be real, and not “acted.”
Clearly, this lends itself more to dramatic roles than anything else. We live in drama every day and can often produce experiences similar to those in dramatic scripts. The same is not true of, say, slapstick comedy or science fiction or a stylized musical.
What’s tricky about method acting is there’s a very common misconception about the term, and it’s become much more accepted than the reality. It’s been a bit co-opted.
The misconception is that the actor should inhabit the role off-screen as well, for the duration of the performance. This gave rise to stories about actors staying in character during an entire film shoot, sometimes resulting in wild on-set stories. However, this wasn’t originally part of The Method. This particular angle was more popularized by Strasborg.
Over time, the phrase has come to be shorthand for “serious” or “dramatic.” A “method actor” specializes in dramatic, emotional roles where they try to bring a sense of realism to the role.