The cell organelle that fuses with a vesicle for purposes of digestion is the lysosome.

Here's why:

* Lysosomes are membrane-bound organelles that contain powerful digestive enzymes.

* Vesicles are small, membrane-bound sacs that transport substances within the cell.

* When a vesicle containing material to be digested (like food particles or worn-out cell components) approaches a lysosome, the two membranes fuse.

* The digestive enzymes inside the lysosome break down the material within the vesicle.

This process is called phagocytosis for engulfing solid material and endocytosis for engulfing fluids.