I understand a normal to indicate the following information:
normals are intersections which are perpendicular to the plane of your face
I understand this to be a vector. And that a shader uses this information to calculate how to render something to the screen. For instance, whether this plane would reflect light to the camera or not, which of course depends on its orientation. (Correct me if I am wrong).
Then I read that a vertex, by itself, can have normal data. This I do not understand. Maybe I completely miss the point and context, but: How can a single vertex, not being part of a line (or a plane), indicate a normal? I mean, a single vertex is dimensionless right. Would its normal not always come from the planes surrounding it? So it is more of a derived value, instead of an intrinsic value of the vertex itself?