In most games, a normal jump is the kind of jump one performs when simply inputting a jump direction on the ground, doing nothing special in particular.
In a King of Fighters context, a normal jump is performed by hitting one of the jump directions ( , , or ) and holding that direction a little longer than “instantly”. This jump is slow and high.
The primary uses of the normal jump (since its obviousness means it is an open target when used without a purpose) include crossup attacks from close range, as an accent to attacks from small jumps during rushdown, and for air-to-air attacks using a vertical jump.