I think more specifically, it means being able to perform a jumping attack that recovers fast enough to block, in the event that your opponent performs a "wake up" attack or counter attack (if in stagger state).
Basically, if they try to attempt any move, and you perform a safe jump, they're attack will be blocked 100% of the time. But if they miss time their attack, you nail them.
Factors here include, the recovery of your jumping attacks and how fast your opponent's attack comes out.
The "Safe Jump" you are describing is the traditional Street Fighter term. This technique (more or less) does not exist in MK9 since the opponent can hold down when on the ground to change how long it takes to get up making it only a guess instead of an insured situation.
In MK9 terms, "Safe Jump" refers to the stagger state that is the result of some certain moves connecting. When hit by one of these moves, the opponent looks similar to "dizzy" state in other games. The biggest difference is that they can block the whole time, but do nothing else. This usually results in being able to do a jump-in attack (preferably punch) to force them to block, then continue with a throw or mixup strings. It gives you a free chance for a mixup. The duration of the "Safe Jump/Stagger State" varies for some moves.
Some characters have unblockable moves that they can use after acheiving the "Safe Jump/Stagger State":
Nightwolf: f2 > Exqcb3, juggles to combo
Cyrax: b1212 > ff4, dash 22, unblockable bomb trap to combo
Quan Chi: db3 > 21~Exdb1, unblockable Rune Trap (can be repeated since the Exdb1 also gives Safe Jump/Stagger)
Most Safe Jump/Stagger moves however do not have such a high reward, but instead allow you to continue your offense with the opponent's only option is to block. I hope this helps.