A vesicle is a bubble of liquid within a cell. More technically, a vesicle is a small 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. Vesicles are also more commonly known as nuclear membranes, because they're very similar to the cell membrane.
They can be found in animal cells.