I cannot start my next task until the other person completes his task. I need a good word to publish this to senior management.
You are waiting for a task preceding yours on the critical path to be completed. As @Ste suggests in his comment above, you are waiting for a task on which yours is dependent to be completed.
The point about using the concept of the critical path is that critical path analysis is a respected project management technique and no task on the critical path can be started until the one(s) on which it is dependent have been completed.
Blocking or blocked is a term generally used in software development for a task that cannot be completed due to something else needing completion first. It is in such widespread use, it is a "feature" in the popular team collaboration software Rally. One would mark a task as blocked in your scenario.
Another term is prerequisite. This is often used in the description of an educational course where certain courses are required to be completed before starting the course described.
Consider idle time [Investopedia]
Idle time is unproductive time on the part of employees or machines as a result of factors beyond their control. Idle time is the time associated with waiting, or when a piece of machinery is not being used but could be.
You might consider describing this state as being in limbo. In this context it basically means that you are trapped at a certain point waiting for something to occur so that you can move on.
This is not a perfect fit, as it also suggests that the outcome is uncertain, whereas in your case, the outcome is certain, you just need someone else to finish something.
Often this is referred to as a
Holding Pattern (M-W)
1 : the usually oval course flown (as over an airport) by aircraft awaiting clearance especially to land
2 : a state of waiting or suspended activity or progress
The first entry is the literal definition, while the second is a common figurative usage, particularly in business scenarios.
It is called "lag time"
Lag Time is the delay between the first and second activity. For example, the time duration for the first activity is 3 days, and for the second activity it is 2 days.