Basically raw files are picture files consisting of the raw data right from the sensor, with no processing applied. When you shoot in jpeg mode the camera compresses the file and applies color adjustments, sharpening etc. (depending on your settings). That is the most basic difference. Working with raw files adds steps to your workflow-- that is the downside. The additional steps involve converting the raw file to a jpeg or tiff file (the two most common image formats). The upsides are big- you can make your white balance adjustments during that conversion process, plus you can make other exposure and color adjustments if you want to. But for aquarium photography the big deal is being able to adjust the white balance on your computer, after the picture has been taken.
Your camera came with raw conversion software, plus Photoshop and other programs can convert raw files.