More generally, phagocytosis in the capture of a solid external to a cell in a membrane which is then brought inside a cell by active transport.
To add to Eos's node, phagocytosis is not just for ingesting food. It is used by certain types of white blood cells (eg, marcophages) as a defensive mechanism in the human (an probably many other animals') immune response. These cells extend pseudopodia to surround pathogens and then engulf them and break them down using lytic enzymes.
Some types of really nasty pathogens are resistant to the lytic enzymes and can live and reproduce inside white blood cells.