What is P Wave Symmetry and Its Role in Super Conductors?

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It has to do with the "shape" (symmetry) of the superconducting wavefunction.
Most conventional superconductors have s-wave symmetry which means that the wavefunction is isotropic. High-Tc superconductors have d-wave symmetry meaning the wavefunction has four "lobes" (in k-space). This means the properties (the "gap") of the superconductor will depend on the orientation of the crystal.
P-wave means that the wavefunctions has two-lobes.
The letter s,p and d have been used to indicate symmetry in atomic physics for a long time (initally it referred to the appearance of the line when doing spectrscopy d=diffuse), see the image on the right on the folllowing wiki.
https://en.wikipedia.org/wiki/Atomic_orbital