Vectors are physical quantities which require both magnitude and direction for complete description.
ie vectors are quantities that have both magnitude as well as direction.
Eg:
Velocity is a vector quantity since it has both magnitude (numerical value) and direction. If you are saying that the velocity of a certain object is 5 m/s, it is incomplete since the direction of velocity is not mentioned. Velocity could be in any direction, so a certain direction has to be assigned to it in order to give complete information.