A computer monitor is essentially a small, thin LCD or OLED panel, and like any flat screen it must travel upright and protected. The glass flexes easily and the stand can twist or snap if packed carelessly. With the panel padded and boxed upright, a monitor is one of the easier fragile items to move.
Pro tip: Most modern monitors have a quick-release stand. Detaching it makes packing far easier.
Watch out: Never transport a monitor lying flat. Pressure on the panel can crack the display internally.