The graphic below shows an object that has been shifted from an upper right position to a lower left position. In the process each of its points gets moved to a new location. We may describe this using arrows, one for each point that gets moved. The tail is at the point before the shift, and the tip is at the point after the shift.
As we see, all of these arrows have the same length and direction. So, we bundle them all together into a new object, called a vector. In other words, a vector consists of all arrows of a given length and direction. As a consequence, it contains all arrows necessary to move any object in the given direction by the given distance. This explains the term ‘vector’ = carrier.