First of all, definitely not a stupid question! To my knowledge, the process of keeping everything sterile is pretty much just to prevent bacteria etc from getting into your surgical site where they shouldn't be, and causing an infection. Off the top of my head I can't think of any other major reasons for why everything will be kept sterile, although someone may well jump in with something I've forgotten!
Well you've said it yourself - infection. Say you're doing a spay, or another intra-abdominal surgery. If bacteria get into there, then you risk the animal developing peritonitis which can potentially be fatal.
Gowns and gloves will be more sterile than just gloves, as there's a risk that if you're not gowned up then your arm above the glove could touch the site, or your sterile instruments/drapes. And even if you've scrubbed up to the elbow, as is best practice, your arm still won't be completely sterile. When I was taught about sterile practice in my third year (last year), we were taught that wearing long sleeved gowns is best practice. Some practices will still use short sleeved gowns, which prevent any contamination from your clothes but not your arms.
Hats is about preventing physical contamination by preventing hair from falling into the surgical area. I also sometimes wear a mask over my mouth and nose when I'm in theatre but this tends to only be when I'm feeling a bit ill and am concerned I'll cough or sneeze on the sterile area. They're also standard PPE to wear during dental procedures and my practice had a policy that everyone in the room, including nurses and students should wear a face mask during dentals.
Well it depends to some extent what these vets weren't doing, and for what procedures. At the practice I've done a lot of placement at, cat castrates typically weren't done under such strict sterile conditions, in that they weren't done wearing gowns, only gloves and they'd be done in the prep area as opposed to taking them through to theatre. That's pretty much the only 'proper' operation that I can think of that has relaxed sterility - on the small animal side anyway. Farm animal operations are often done under less than ideal conditions on farm, but that's a whole other issue!
Anything more involved than a cat castrate, such as dog castrates and anything that involved going into a body cavity such as spays, exploratory laparotomys, should as far as I know be done under full sterile procedure so gowns, gloves, etc. Then from my understanding, although I haven't started this yet, orthopaedics is another level of sterility again! At my university's teaching hospitals, the equine building has two operating theatres I believe, one 'dirty' one for soft tissue surgery such as colics, and then a 'clean' one which is used for orthopaedic surgery. Don't quote me on this because I haven't started orthopaedics yet but my understanding is that if you get an infection in a bone or joint it's a complete nightmare to treat, so orthopaedic surgery should absolutely be done under the most sterile conditions possible.
I hope this helped a bit
If there's anything I didn't explain very clearly or if there's anything else you want to ask, please do!