I have heard somebody saying aw, shucks.
- What does that mean?
- In which other cases is the word used?
The word "aw" in this case is an interjection with the following definition (from Merriam-Webster):
used to express mild disappointment, gentle entreaty, or real or mock sympathy or sentiment
If something mildly bad (but not too bad) happens to someone else, you can say "aw". (If it is something really bad, then it sounds rude to say "aw".)
It that case awe means nothing. It is a particle. Kinda like the oh in Oh... that's bad.
"Aw, shucks" together form an extremely mild expletive to express disappointment or frustration. Think "Oh, damn" for kindergartners. It's also used to indicate false modesty, something a cartoon character says while blushing after being complimented. It carries a little bit of a rustic, unsophisticated flavor. I've seen it applied to politicians affecting a humble demeanor.