In RAW shots you retain a lot more data. Now whilst Lightroom lets you do a lot to JPEG that it will do to a RAW, the results can and will differ.
As an example if you just clip the whites in a shot, so that its just overexposed. If you hvae the shot in JPEG you won't have any data at all to restore; you can slide the exposure and brightness sliders, but there won't be anything there. In a RAW shot you will have more data present; you'll be able to recover a little more (though not a vast amount - if you over or under expose fully the camera only records white/black data).
You can also see it in background areas, sometimes you might get "lines" appear in the blurred regions which is called banding. In a JPEG this happens because the values for the colours are simplified significantly; thus when you edit and cause them to change sometimes the difference between two spots, even if next to each other, becomes more significant (the "numbers" that make up the colours are more rounded up/down).
In a RAW you've got a lot more colour data, so the transitions are smoother and thus you can push and pull things and the transition will remain faint and smooth.
RAW retains significant portions of information which makes it far more valuable and far easier to edit with. Even if you're not doing extreme things.
Further RAW is a lossless format which means the data is preserved between saving - actually with RAW the original file is never changed, RAW processing software makes a separate file in which it stores all the changes made to the RAW - this is because you can't save a RAW - its not an image format*. Thus whenever you save a RAW as an output it will be in another file format - like a JPEG or TIFF.
JPEG is a lossy format which means each time you save some data is lost. Do it enough times and you can start to see the effect (and edit and it shows up even more).
* the image you see when you view a RAW on your camera, or on software like windows picture viewer and the thumbnails in the file - all those are a JPEG that is made and embedded inside the RAW (there is even software out there which can extract the JPEGs from a RAW). Again this is because RAW is not an image format; thus the camera has to show you something so it processes a JPEG (to its set in-camera editing settings). This is why even if you use RAW you should keep in-camera editing settings to faithful/neutral so that you are reviewing as close to the RAW as you can when previewing on the LCD on the back of the camera.