The process called when a cell engulfs a particle is known as phagocytosis. This cellular mechanism allows specialized cells, such as macrophages, to ingest larger particles, including pathogens and dead cells. During phagocytosis, the cell membrane extends around the particle, forming a phagosome, which then merges with lysosomes to break down the ingested material. This process is crucial for the immune response and maintaining bodily functions by clearing away debris.