How to describe the "waiting time" as someone else has yet to finish the dependent task?

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.