The characters in The Silence of the Lambs basically go from point A to point B, with a few skinned corpses, creepy moths, and transvestite solo dance numbers along the way. Occasionally, the film uses a flashback method to show us Clarice Starling's youth—greeting her dad when he comes home, or her dad's funeral— but the power is in the close-up. In Clarice's big speech about the screaming of the lambs, Demme initially wanted another visual flashback, but decided that Foster's performance carried the story better than any picture of a lamb could. (Source)
Besides all the horror and funky face masks, The Silence of the Lambs is ultimately a film about control. Like any serial killer, it's a cat-and-mouse chase. Except Silence of the Lambs makes it cat, mouse, and cannibal, throwing Hannibal Lecter into the mix. The person in charge seems to change minute-by-minute. This is reflected in the controlled way the film was shot, featuring many close-ups of not just Foster but all the actors, and many scenes of actors speaking directly into the camera as if they are speaking directly to the viewer and drawing you into the action. (Source)
If you ever find yourself ready for your close-up with Hannibal Lecter, make sure to not get too close.