The transport process that cells use to direct the contents of vesicles out of the membrane is called exocytosis.

Here's a breakdown:

* Vesicles: These are small, membrane-bound sacs within the cell that hold various substances like proteins, hormones, or waste products.

* Exocytosis: This process involves the fusion of a vesicle with the cell's plasma membrane, releasing its contents into the extracellular space.

Essentially, exocytosis acts like a cellular "delivery service" that allows the cell to release substances that it has produced or ingested.