I've looked quite a lot on shaders lately and one thing that confuses me is all the abbreviations and what they mean and do. Abbreviation might be wrong since most are just single letters but things like Oi = Os, Ci, P, N, s, t are those I've seen the most. I've been trying to find a list of all these, how they are used and what they do but have been unable to find anyone so can someone please help pointing me in the right direction.

I couldn't tell you about the Oi, Os, Ci or P (these are most probably names assigned by the creator, so will only have meaning in context).

N is almost certainly a Normal vector.

And s & t refer to dimensions in a 2D Texture (horizontal and vertical respectively) - similar to the X, Y coordinates of vertices.