Lysosomes are a type of vesicle. Vesicles are spheres surrounded by a membrane that excludes their contents from the rest of the cytoplasm. Vesicles are used extensively within the cell for metabolism and transport of large molecules that cannot cross membrane unaided.
Lysosomes are specialized vesicles that contain digestive enzymes. These enzymes can break down large molecules like organelles, carbohydrates, lipids, and proteins into smaller units so that the cell can reuse them. Therefore, they are like the waste disposal/recycling department of the cell.