A substance is said to be optically active which it can rotate a plane polarized light. Such substances are chiral molecules. The reverse is true for optically inactive compounds.
If you look at the carbon center in 1-bromobutane it has two hydrogens attached to it and hence it has a plane which can divide the molecule in equal half, i.e. plane containing C3H7−C−Br, hence the carbon center is achiral and is optically inactive. On the other hand, the carbon center in 2-bromobutane has four different groups attached to it and hence do not possess a mirror plane, so we can say that it is chiral or optically active.