The Jetpack upgrade is unlocked once the player completes Ghost Hunter Riley's 15th and final quest
The Jetpack "greatly increases vertical mobility" and activates once the jump button/space bar has been held and the initial jump has (or at least should have) ended. (i.e. to use it, just hold your jump button/space bar)
The Jetpack can also be used with the Hoverboard, allowing the user to pull off more than one jump (on the Hoverboard) midair, similar to the Ghost World, but it only grants the user an extra jump.
The Jetpack literally grants the user another jump after the first one has reached its peak (i.e. once your initial jump reaches its highest point, the Jetpack boosts you with another jump)
And, with the exception of using it with a Hoverboard, the Jetpack cannot activate midair.