Vector is a concept introduced to exactly explain the behaviour of a particke. For eg, supposing u hav a body moving in the XYplane, to locate the instantaneous position, u need its co-ordinates. But, they dont exactly tell u the would be position, i.e, u dont know its direction. To make such aspects clear, we use a quantity that shows both its magnitude and direction. People call this a VECTOR. Dimensions are the regions u divide the space into so as to express ur views about the behaviour of a particle clearly.