Final answer:
The cell membrane is the part that allows or prevents substances from entering or exiting the cell, due to its selectively permeable nature.
Step-by-step explanation:
The part of the cell responsible for allowing or preventing substances from going into and out of the cell is the cell membrane. This structure acts as a barrier, separating the cell's interior from the exterior environment. The cell membrane is selectively permeable, which means it allows certain substances to pass through while blocking others, due to the phospholipid bilayer and embedded proteins that make up its composition. This feature of selective permeability is crucial for maintaining the proper balance of molecules inside the cell, ensuring that essential nutrients come in and waste products go out.