The Sounds of Silence
The score is one of the most memorable parts of the movie: Simon and Garfunkel's soundtrack echoes Benjamin's own alienation and worried melancholy with songs like "The Sound of Silence" and "Scarborough Fair." On the other hand, "Mrs. Robinson" is much more lighthearted—an ironic tribute to the artful seductress.
In fact, that was the only song written specifically for the movie, and it originally referred to "Mrs. Roosevelt" instead of Mrs. Robinson, being about Eleanor Roosevelt, Joe DiMaggio, and nostalgia for an earlier time. Paul Simon was apparently a pretty slow, painstaking songwriter; his original agreement to write three songs for the movie had fallen through. But Nichols had become a fan of some pre-existing Simon and Garfunkel tracks, like "The Sound of Silence," and used those instead. The use of existing popular music as the soundtrack was a real break from traditional film scoring.
Writer Sam Kashner, perceptively points out:
"Simon and Garfunkel's lucid, poetic lyrics serve as Ben's interior monologue as he makes his way through the empty opulence of his parents' suburban paradise. The juxtaposition of 'The Sound of Silence,' a deeply personal cri de coeur, against the Los Angeles airport terminal—as Ben is carried robotically along a moving walkway—is both touching and funny." (Source)
Benjamin is experiencing the "sound of silence" because he's living in a mental cocoon, drifting on his pool, sleeping with Mrs. Robinson, but not really connecting with anybody. Even though he outwardly seems like a bright, privileged kid who should be thriving in the world, he's internally unsure and conflicted—and inert. Like Kashner points out, Simon and Garfunkel dip into this deeper undercurrent of emotion; the sad inner life existing behind the seemingly idyllic outer life. Pay attention: it's the song played during the last scene on the bus, as well. Maybe all's not well that ends well after all.
(Fun fact: Nichols rejected two Simon and Garfunkel songs which Simon actually did write for the movie, "Punky's Dilemma," and "Hazy Shade of Winter," the latter of which appeared on a greatest hits collection (Source)