This process is very similar to pinocytosis, the only difference being that the material surrounded by the membrane is not diluted.
While pinocytosis is a process common to almost all eukaryotic cells, many cells belonging to multicellular organisms do not perform phagocytosis, but are made by specific cells. In protists phagocytosis is often one of the forms of food intake.
White blood cells use this process to surround foreign materials like bacteria or even damaged cells. Within the phagocytic cell, cytoplasmic enzymes are secreted into the gallbladder and degrade the material to a harmless form.