We all (I think I can safely say all) feel silly reading our writing aloud. Especially if one's spouse/child/roommate is sitting there smirking and/or laughing their ass off. However, I completely value the importance of it. And reading really quickly under your breath doesn't count.
So, if you are wise enough to read your book aloud, slowly and carefully as if you were reading in a public setting, you might discover things like glaring errors from when you edited the heck out of your first chapter fifty million times and accidentally removed a reference to an object on the first page that then abruptly and nonsensically appears and makes no sense whatsoever on the second page. It would also help you avoid run-on sentences like that one.
Of course, it's extremely helpful, dandy even, if you read your work aloud and discover this before you submit your manuscript to ten agents, including one that requested a full. Your first request for a full, mind you. However, in the event that you don't discover this before submitting to ten agents including one that requested a full, there are other options involving bullets, rope, cliffs, poison, daggers, mass quantities of alcohol...
*Enormous sigh* So, does anyone else want to share a really embarrassing story?