If I place set of axes on the arrow I can divide the field into two components of the field, namely the x component and the y component. the longer the arrow, the stronger the field. The length of the arrow can be thought of as the strength of the field, i.e. The direction of the arrow can be thought of as the direction of the magnetic field. This means there is a direction associated with the field as well as a field strength. The magnetic field at any point in space is a vector quantity.
