Cameras that produce JPG files do some processing in-camera, then compress the files so they take up less space on the card. The problem is that they "trow away" a lot of useful image information that can't be retrieved later. RAW files are like a "digital negative". They contain every tiny bit of information the sensor captured. BUT they take up a lot more room on the card, AND they need to be processed in some sort of image editing software (typically Photoshop or Lightroom) before you can do anything else with them.
The advantage, in a situation like this, is that with good software, you can recover details in the highlight and shadow portions of the image that would be lost by in-camera JPG processing. Most, if not all, DSLR's can shoot in RAW (or Nikon uses another name for the same thing) there are only a very few, high end, P&S's that can capture RAW images.
That said, in this specific picture, Suzi, you've done a very good job capturing the tonal range from light to dark. Because you shot her in strong, filtered light, with no direct sun on here, you have almost complete tonality, in her dark and light areas. You can't see her eyes mostly because of her hair, not because the photo is too dark!