Final answer:
A membrane that allows selective substance transport, known as a selectively permeable or semipermeable membrane, is essential for cellular function.
Step-by-step explanation:
The type of membrane that allows some, but not all materials to cross is known as a selectively permeable membrane, or semipermeable membrane. This selective permeability is a critical feature of plasma membranes in cells, which need to regulate the transport of substances to maintain cellular function and integrity. Semipermeable membranes may have small pores to control the passage of small molecules or may involve specific processes whereby molecules dissolve in the membrane or interact with it to move across.