RAW: the digital negative

The RAW is the only file format that allows to fulfill the potential of the camera; it is a kind of "digital negative", since is provides an unprocessed image that must be optimized with an image editor before being printed or published on internet.  
 
RAW is not a single file format. Every manufacturer uses a proprietary RAW format: for example, the Canon's RAW is .cr2 ; Nikon's RAW is .nef ; Olympus's RAW is .orf , etc. Other than that, every camera has a slightly different RAW format, so if you buy a recent camera you may not be able to open its RAW files until the raw converter of your post processing program has been updated to support the file format of the new camera.  
 
RAW files are almost unprocessed; you can change many image parameters (contrast, sharpening, colors space, white balance) when you open the file with your raw converter. This is one of the great advantages of RAW: for example, if you accidentally apply an exaggerate in-camera sharpening to the RAW file, you can correct it. With JPEG, instead, there is not way to correct in-camera oversharpening and other errors.  
 
Another advantage of RAW is the bit depth: RAW files are 12 or 14 bit, while JPEG is 8 bit. The bit depth is an important attribute of every image format; it specifies how many bits are used to create a color, and then how many shades of color can be represented. The bits are the basic units of the entire digital world. A computer understands just two values : 0 (off) and 1 (on); and a bit is right that : a 0 or an 1. To get more values, you have to combine more than one bit. With two bits, you have four (2²) values : [0,0]; [0,1]; [1,0]; [1,1]. Three bits correspond to 2³ -> 8 values, 4 bits-> 16 values, etc. A commonly used bit depth is 8 bit, that has 256 values per channel. Other bit depth used in cameras and scanners are 12 bit (4096 values) and 16 bit (65536). These values are referred to just one color channel: if you consider all three channels (red, green, blue), you have 16,8 millions of tonalities with a 8 bit image, while a 16 bit image has 281474,9 billions of tonalities! The obvious advantage of high bit depth is that you you can represent much more subtle color tonalities and you can make heavier adjustments during the post processing; other than that, you need a wide bit depth to store the entire dynamic range that the camera is able to capture.  
 
These crops show the advantage of RAW vs JPEG.

 

The image A is a crop taken from a very dark shadow area of a photo. The image B is the same crop, taken from a JPEG image and brightened up with levels to show some detail. The image C is the crop taken from a RAW image (14 bit) and brightened up by about 4 stops. The colors and the detail in the RAW photo are much better, the image is sharper and it has more natural colors.  
 
Let's see an example in opposite situation: a very overexposed area.

 

When you have to recover highlights, the difference between RAW and JPEG is huge. Image A is a crop from the original photo, overexposed by about 3 stops. B is the image recovered from JPEG, while C is recovered from RAW: the raw version is much much better, it has recovered a lot more detail and it has a more pleasing look.  
 
If you do nature photography, you should always use RAW as in-camera file format. JPEG is a great format for internet, but it does not give the same quality of RAW. Sport photographers or photo journalist can trade some image quality for the faster workflow given by JPEG files, but for nature photographers there is not any reason to shoot in JPEG: the only "advantage" of JPEG is the smaller file size, but nowadays memory cards are cheap and they offer huge capacities.  
 
In the latest years, some cameras have added a "sRAW" mode, that is a RAW file at reduced resolution. I recommend to avoid this useless file format: you don't get any advantage and you just lose resolution. The noise is the same that you get by shooting in full RAW and downsizing with Photoshop, and, even though the file size gets a bit smaller, it is not a big advantage because with today's memory cards storage space is no longer a problem.