Final answer:
The process where cells in a developing zygote begin to specialize is known as differentiation. This follows a series of rapid cell divisions called cleavage which leads to the formation of various tissues and organs.
Step-by-step explanation:
The correct term for the process described, where cells in a developing zygote begin to take on specific roles, is differentiation. After fertilization has taken place and a single-celled zygote is formed, it undergoes cleavage, a series of rapid cell divisions. The cells that result from this division are initially similar, but as development proceeds, these cells undergo differentiation to become specialized in structure and function for various tissues and organs within the organism. This process is a fundamental aspect of the development of multi-cellular organisms and is crucial for the proper formation of the organism's body plan.