The LCD screen on the back of your camera Lies like a politician! They are designed to make every shot look as good as possible so when you look at them at the store you will say, "This camera takes really good pictures!"
Remember, typical DSLRs now have resolutions of around 20MP, give or take a few. The LCD screen on the back of most DSLRs is about 1MP, give or take a few. What this means is that blur that is less than about 5 pixels wide (or high) will be combined into a single pixel on the LCD preview screen and will appear to be sharp!
Preview images displayed on your camera's LCD screen are also sharpened and usually have a bit (or more) of contrast and saturation added to give them a little "punch". Hey, the camera manufacturers want that preview image to look incredible when you make a sample snapshot under the crappy light at the camera store!
Keep in mind that if you are saving raw files, you're not viewing raw data on your camera's LCD. What you are seeing is the jpeg preview image generated by the camera that is appended to the raw data in your raw file. When you open the raw file on your computer your viewing application probably isn't using the same settings to render the raw data into an 8-bit JPEG-like image on your computer's screen. For more about the different ways cameras and computers render the same raw data, please see: Why do RAW images look worse than JPEGs in editing programs?