A vibration is IR active if there is a change in the dipole moment and Raman active if there is a change in polarisability due to that vibration

Polarisability

The concept of polarisability is not as obvious as dipole moment. When a molecule is placed in a static electric field, the nuclei are attracted towards the negative and the electrons towards the positive pole. This separation of charges created by the external field results in an induced dipole moment. If E represents the strength of the electric field and p denotes the induced moment then p = a E, where a is the proportionality constant called polarisability, p and E are vectors, the magnitude of the induced dipole moment will be different for each of the components of the electric field. Resolving p, and E in the x, y and z directions we get the simple relations.

But for most molecules this equation is not valid as the direction of polarisation does not coincide with the direction of the applied field. This is because the direction of chemical bond in the molecule also affects the direction of polarisation, the relation above therefore is represented as:

The nine coefficients a_xx, a_xy…..are known as the polarisability components.