Monitors (and televisions) rely on magnetic fields to direct the beam of electrons to the appropriate spot of phosphur on your screen to display a color. If the beam is deflected even slightly off target, it will illuminate the phosphur next to it instead (so instead of a red "pixel" lighting up, you might get a blue).
There's a whole process performed at the factory of adjusting the monitor's magnetics in order to get good purity and convergence, which involves precise positioning the yoke and adjusting 4-pole magnets on the neck. While making this adjustment, it's important that the monitor is in the same orientation that it will be during use, because the Earth's magnetic field also plays a role in how the electron beam is deflected.
If you change the orientation of the monitor after purity and convergence is set, you can expect the Earth's magnetic field to act differently, and will see some areas of the screen where the color appears off-tint. This might resemble the need for degaussing, but it is not the same as part of the monitor becoming magnetized (which also causes deflection problems that illuminate wrong phosphur).
This effect becomes more noticable with smaller dot pitches, because each phosphur color is closer together, so small amounts of error produce more dramatic results. To illustrate, take the computer monitor that you're looking at now, and turn it sideways.