What term describes the movement of broken-up pieces of rock?

The term that best describes the movement of broken-up pieces of rock is "Erosion." Erosion is the process where soil and rock are removed from one location and transported to another by natural forces such as wind, water, ice, or gravity. When rock is weathered – that is, broken down into smaller pieces – erosion is what enables those pieces to be carried away from their original location.

Weathering, while related, specifically refers to the breaking down of rocks and minerals at their location without movement involved. Transportation refers to the actual movement aspect, but erosion encompasses both the processes of wearing away and transporting materials. Deposition refers to the process where eroded material is dropped off or settled in a new location, occurring after erosion has taken place. Therefore, erosion is the correct term that encompasses the movement of broken-up pieces of rock.