A vector is a directed segment.
For vectors adding the parallelogram rule is used: the sum of two vectors with common beginning is represented as a diagonal of a parallelogram constructed on these vectors.
The movie explains the rule on the example of parachutist's velocity vectors. The parachutist is diving down with the velocity V1 and the velocity of a side wind is V2. They are added using the parallelogram rule. The resulted velocity of the parachutist V isn't a vertical. He lands far from the point of the original direction.