Calibration for Final Viewing
Calibration for final viewing is actually more obvious, as without it you will never be seeing images as the production team, specifically the DoP, intended, which greatly reduces the impact of the viewing experience as much of the emotion in any moving image is portrayed through the use of colour, even if that means removing colour...
Most consumer home TVs and projectors are obviously made to a budget to compete within their sales market, and are factory configured to 'stand-out' on the show-room floor. None of which attributes to final image accuracy, distorting the original intent of the production company responsible for the original media content.
Therefore, display calibration for final viewing is the process of adjusting a display's settings, often through the use of an external LUT box, so that the viewed images match as closely as possible the colour standards used for initial video mastering, enabling the original artistic intent to be viewed, preserving the emotional content, and so maximising the intended viewing experience.
Calibration is based on matching industry video standards that define how an image should look on any given screen when accurately matched to the given standard.
Unfortunately, nearly all home TVs are provided with very poor 'factory' calibration out of the box, with over saturated colours, widely inaccurate gamma and colour temperature, and incorrect black and white levels, with such settings aimed at 'looking pretty' in the TV show-room.
'Showroom' settings are anything but 'accurate', and demand the TV be accurately calibrated before any images will look as the production intended.
Basically, the aim for all calibration is to make the home TV or projector behave as much like a professional grading monitor as possible, ensuring the full impact and emotional intent of the viewed media can be enjoyed to the full.
Factory Calibration Inaccuracy
It is very important to realise that no 'Factory Calibration' for any mass-market display or TV is ever 'good'. Even those aimed at the professional market, rather than generic home TVs.
During the manufacturing process the time allocated to calibration is negligible, if any is allocated at all. Most such displays/TVs are just loaded with 'generic' calibrations to get them in the ball-park, based on testing on one unit prior to the manufacturing run. To spend time actually calibrating each individual display would add significant time, and therefore cost...
When you get to more specialised display manufacturers it is likely that more time will have been allocated to calibration, but in reality it will never be performed to as critical a level as an end user performing their own calibration.
Even with the highest-end probes, the level of profiling required, with many thousands of calibration patches being used, will take more time than any manufacturer can allocate.
There really is no alternative to end-user calibration for true display accuracy.