Every phase transition has an order parameter: something that vanishes above the transition temperature and is finite below.
In superconductors, the order parameter is a complex quantity related to the superconducting gap: $\Delta = |\Delta| e^{i \phi}$.
In BCS theory, there is a self-consistent equation for the gap:
$\Delta_k = -\sum_q V_{kq} \frac{\Delta_q}{2E_q} \tanh \frac{E_q}{2 KT}$.
At this point BCS made the assumption that $V_{kq} = -V$ (the interaction potential is momentum independent and attractive) leading to $\Delta_k = \Delta_q = \Delta$ (i.e., also momentum independent and constant). The gap has the same value at all positions of the Fermi surface. It is the so-called $s$-wave (isotropic) gap.
Now, if one does not make the approximations in $V_{kq}$ then funny stuff happens. For instance, if $V$ is positive (hence repulsive) you can still have superconductivity! But this means that the gap must change sign (note the minus sign in the self-consistent equation). And this change will happen in momentum space directions where the interaction potential is large.
A particular case of this gap sign change is an order parameter with $d_{x^2 - y^2}$ symmetry. This is a gap that will change sign at $(k_x,k_y) = (\pm\pi,\pm\pi)$ directions in momentum space. It is the currently mostly accepted symmetry for cuprate superconductors.
This symmetry is not necessarily that of the paring potential. What is required is that the pairing potential must have a large value close to $(\pm\pi,\pm\pi)$ directions.
The still unanswered question is what is the pairing potential, though.