Quick question for photographers- RAW?

Hello! First, feel free to go to the bottom to read the question if you don't want to read. It's not essential, just background info.

I'm going to be event photography for a conference for a few days coming up. I got in touch with the person incharge of advertising and she basically said she was disappointed in the images from the past few years. I tried to explain to her that I'm at the mercy of the quality of my equipment, the lighting and the distance I have to keep between me, the participants and the horses. I pray the horse arena will be outside, but its doubtful! The rest of the conference is in conference center in a hotel.

The other thing was that the photos weren't large enough. She wants them "large" enough for full page ads. Assume what she means is that some (well probably a lot) of the images were grainy, which I really can't help working in low light with moving objects. She told me I need to set the quality of my photos higher. It's always on the highest possible without setting it to RAW.

So I guess, in short, my question is what exactly is RAW and would the photos be better quality if I shot using RAW?

Also, any advice on photography in less then ideal lighting would be much appreciated!

If it helps any I have a Canon Rebel xS, 10.1 megapixels, a 55-250mm and a 18-55mm, and a speedlite 430ex II flash.
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RAW as far as I know it is better to work with when editing....hmmm I think that's right! Someone else will probably come and correct me!

Yes, RAW is used if you want to fiddle with the photograph heavily (ie white balance or other major photo manipulation, not standard editing). I was taught to use the largest, least compressed JPEG for the vast majority of my photographs.

I've been taking pictures in the indoor this winter. I've had good luck with an ISO of 6400, setting it to the lowest aperture and letting the camera choose the appropriate shutter speed. But, the higher the ISO, the more grainy the pictures so try and go with the lowest ISO you can get away with.

I don't know if any of this helps or is stuff you already know. I just took a photography class, so I'm sort of currently geeking out with my camera =) I can't wait until summer hits and I can start taking pictures outside at shows.

I'm not looking to edit them any further then croping, fixing the contrast/color, and straightening. The people I'm "working" for (its more like an exchange, I'm not being paid) said they needed larger and higher quality images. My camera is already on L, the next would be L RAW. So besides editing would it make a difference for them printing and publishing wise?
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I would definitely suggest shooting in RAW - I ALWAYS do. Mind you, I have done that ever since I first got my camera so maybe I'm just stuck in my ways lol.

Shooting in RAW makes sure you capture all of the data that hits the sensor, whereas setting to a lower quality means that you eliminate a bit of the data.

I just did a google seach and found this: 10 Reasons Why You Should Be Shooting RAW | Photography Concentrate

It basically explains a few reasons why you should try shooting in RAW

I figure it'd probably just a good idea to always shoot in the highest quality setting that you can, even if it means buying another memory card!