The something is the superconducting order parameter, which is loosely $\Delta_{\alpha\beta}(r-r')=\langle\psi_\alpha(r)\psi_\beta(r')\rangle$ where $\psi_{\uparrow(\downarrow)}$ is the operator that annihilates a spin up (spin down) electron. Now $\Delta$ must transform under the symmetry group of the crystal. So the terms $s, p, d$ and all their ilk refer to the possible representations.
Except that $s, p, d$ and so forth label representations of $SO(3)$, whereas $\Delta$ should transform under the point group $G$ of the crystal, which is a discrete subgroup of $SO(3)$. So a single irreducible representation of $SO(3)$ like spin 2 (aka $d$) actually may break up into multiple irreps of $G$. So the usual language is somewhat confusing, but any lengthy paper should define precisely what it means.