Now, ferroelectric materials possess multiple domains. For background on this, read the TLP on Ferroelectric Materials.
To make it simple, we will only consider single crystal ferroelectrics. These, when first made, have domains of the form:
If a mechanical stress is applied to the ferroelectric, then there are domains which will experience an increase in dipole moment and some which will experience a decrease in dipole moment. Overall, there is no net increase in polarisation. This makes BaTiO3 useless as a piezoelectric unless it is put through some additional processing. This process is called poling. An electric field is applied to the ferroelectric as it passes through its Curie temperature, so as its spontaneous polarisation develops, it is aligned in a single direction:
All of the domains in the piezoelectric have a dipole moment pointing in the same direction, so there is a net spontaneous polarisation. Now, when a mechanical stress is applied, the polarisation will increase:
but still remain pointing in the original direction. This makes ferroelectrics into useful piezoelectrics.