There are three reasons:

Color calibration

As we all know, calibrating your monitor is a key part of any digital artist work flow. The problem is, camera LCD can’t be calibrated easily (need a custom picture style) so differences in colors are to be expected to some degree.

Camera LCD are cheap

Even if you managed to balance your LCD with your screen, you would still end up with some differences because the camera LCD cannot reproduce the same color gamut as your computer LCD. This difference is subtle but it is there.

Picture Style

Finally, and this is probably the most prevalent element: images shown on the camera back are processed JPEGs using the camera currently selected picture style. Even if you are shooting RAW, the image appearing at the camera back will be a processed JPG. This is why it is suggested to change picture style depending of what you are shooting, even when shooting RAW, since it gives you better idea of your end result.

This is especially problematic when you are intershooting video clips and pictures since you are probably leaving the picture style to the Technicolor cinestyle which dulls everything.

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planetMitch

chief astronomer at planet5D LLC
Mitch "planetMitch" Aunger is the creator and mastermind behind planet5D.com — which covers every aspect of HDSLR cameras (and a whole lot of other cameras as well). A lover of photography since his early days, he graduated to selling stock photos to make a little bit of spare cash. It wasn’t much, but it allowed him to upgrade to better cameras as well as computers, and it wasn’t taking money away from feeding his family.
He loves the stories that the still image can tell. In the summer of 2008, he read a story written by Arnold Kim called “I Quit My Job” — Arn is the owner of macrumors.com. He started macrumors in 2000 as a hobby, and by 2008 he was making more money with the site than he was on his day job, so he quit. The surprise to the story is that he was a doctor making more than six figures! Right then and there, planetMitch dreamed about doing the same thing.
September 2008 rolled around, and Canon announced this new version of the incredible 5D — the Canon EOS 5D Mark II. It was the first Canon DSLR to shoot full HD video and the earth moved! (It really was a huge deal in the photography world.) planetMitch knew if there was ever a chance to ride a wave of something he was really passionate about, this was it — and the blog at planet5D.com was born. It is now one of the most popular HDSLR blogs on the planet, and he is making a full-time living from blogging. He couldn’t be happier!
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