Here’s the thing: when you go to the movies and laugh, cry, are moved in some way-or maybe just had the time of your life thanks to all the artists that worked on the film...and then you leave the theater and you say to your friends “George Clooney was amazing!”...that’s great; but how great would it be if you could say to George Clooney: “you were amazing”? You know, just say thank you to George, who gave a fantastic performance.
And that’s the magical thing about seeing live theater-you often get to do just that; i.e., say thank you to that wonderful actor who just laid their heart on the stage for you; or made you laugh until you cried; or danced ‘til you thought they would drop.
It’s called a “stage door” and sometimes it’s an actual door-or sometimes it’s a staircase inside a small theater, or a lobby...but the actors have to leave somehow, and, especially in New York in the Broadway community, it is customary for the actors to greet fans after the show as they leave. They will generally sign your Playbill, some will take photos with you and often you can at least exchange a greeting, a thank you or ask a quick question.
And it’s not just on Broadway. It may be a little harder to find the stage door at theaters in other cities; and it may be less expected, but it’s often still possible, if the spirit moves you, to meet the actors. Keep in mind that you might have to be a little braver in those circumstances because there often won’t be the “safety in numbers” that you frequently have in New York. You might have to approach the actor as they leave and ask if they will sign and/or take a photo with you. Sometimes it's nice to have a little one-on-one time with the actors though. I've had some lovely exchanges with actors I truly love and respect (Glenn Close, Cate Blanchett, for example :)).