Intracellular and Extracellular digestion:

Intracellular: In which breaking down of macromolecules takes place within the cell itself.

Extracellular: In which breaking down of macromolecules takes place in outside space of cell including extracellular space surrounding the cell and lumens (free spaces, tubes), etc.

Advantages of extracellular digestion: As in extracellular digestion, bigger molecules are broken down into smaller ones. So, it provide a great advantage to cells in order to take that particles, which cannot be able to enter the cells by phagocytosis,  pinocytosis or diffusion, etc  just because of their large sizes.