When things metastasize, they grow and spread. Cancer cells are said to metastasize when they spread from one part of the body to another.
A cancer patient dreads hearing the word metastasize, since it means that the malignant cells have spread through the body. Breast cancer cells are said to metastasize, for example, if they're found by a doctor in a patient's liver or brain. The process of this happening is known as metastasis. Both words come from the Late Latin metastasis, or "transition," with the Greek root word metastasis, "removal, migration, change, or revolution."