It means that whatever is invading our body is attacked and either phagocytosed or lysed by cells (without the aid of antibodies).
Typically, when students are first taught about phagocytosis, they are told that macrophages in the body can ingest bacteria and destroy them. That is true. However, how does a macrophage know what is harmful (and should be ingested through phagocytosis) and what is not? How can our bodies get rid of cancerous cells that are too large to phagocytose? And can't quite a few cell types actively phagocytose invaders?
I will try to answer these questions in the text below. Keep in mind that multiple cell types can be involved in cell-mediated immunity (CMI). As you read, you will learn that all types of T cells, macrophages, and other cells called natural killer cells are all involved in CMI.