These states are similar to the stand, walk, and run states in that they still use the ground plane for their base. They differ in the fact that they normally don't cycle, instead they start from the beginning and animate to the end. After the cycle finishes they normally go back to the original state they were called from (stand, walk, run) or, in the case of death, just freeze on the final frame.
The 'jump' cycle is called when the model starts a jump action. The feet should start and stop on the ground plane. In-between the legs can move up into the model's body but remember, even if the animation moves the model well above the ground plane, the actual height from the jump comes from the physics in the movement script and not from the model's animation.
The 'attack' cycle is called with the attack action. The proper animation depends on the type of weapon this model will be using. If you plan to use several different weapon types, you may want to write your own attack animation scripts to support each one individually (or 'MORPH' between models).
The 'death' cycle does not normally return to the original state. It should be designed to animate once and freeze on the last frame. It is normally called when the model's health is reduced to zero.