A vesicle is a bubble of liquid within a cell. More technically, a vesicle is a small, intracellular, membrane-enclosed sac that stores or transports substances within a cell. Vesicles form naturally because of the properties of lipid membranes. Vesicles can fuse with the plasma membrane, and release their contents outside the cell. Vesicles can also fuse with other organelles within the cell.
A vesicle is sometimes formed when the cell is doing endocytosis. Endocytosis is a process in which a cell's membrane takes in a particle from the outside and brings it inside the cell with a vesicle around it.