I’ve seen this a number of times in various guises. As far as I can tell, it’s something an actor asks, but what the heck does it mean? The best I could come up with was “How do I do this?”; basically a request for guidance.
Probably the actor is confused what the motivation the character has for acting this way. If the character is angry, why is the character angry?
At least, that’s what my take is. I’ve never worked in film or theater, but it’s a question that comes up when I’m writing a story or something. “Why is this character acting like this?”
Sometimes actors’ scripts don’t have the entire script, just their character’s lines and cues. Seeing a line of dialogue for the first time, the context isn’t always clear, and there are many ways to read any given line.
The question, “What’s my motivation,” invokes a school of acting known as “Method” acting, sometimes called the “Stanislavski Method” after its originator Konstantin Stanislavski, in which the actor steps into and becomes the character being portrayed:
DKW: The question has, to some extent, come to signify preciousness, as in the scenario of the bit-part actor who asks “What’s my motivation?” for a ten-second scene of their emptying a garbage can. And there’s the excellent Olivier/Hoffman story.
When a movie is filmed, it is not shot in the same sequence you see it on the screen. Scenes are shot in an order determined by location, availabilty of cast, etc.
It’s not uncommon to shoot scene 3, then scene 37, then scene 95, etc.
If the actor is working on scene 37, he may need to know that his girlfriend dumped him in scene 36 (which won’t be shot for another 2 weeks) to understand how his character is feeling.