Compute Normal re-computes the normal of the terrain at the point in the network where it is connected. The "normal" of a surface is a vector perpendicular to the surface angle. A computed normal is required for proper application of texture and displacement to the terrain, since both usually depend on the precise shape of the existing terrain. Compute Terrain, which is similar to Compute Normal, provides the initial normal in most scenes and is a part of the default terrain network. If significant changes are made to the displacement after the initial Compute Terrain, the use of a Compute Normal will ensure that subsequent displacement and texturing are accurately placed relative to the true terrain shape.
A vector is a set of three scalars, normally representing X, Y and Z coordinates. It also commonly represents rotation, where the values are pitch, heading and bank.
Literally, to change the position of something. In graphics terminology to displace a surface is to modify its geometric (3D) structure using reference data of some kind. For example, a grayscale image might be taken as input, with black areas indicating no displacement of the surface, and white indicating maximum displacement. In Terragen 2 displacement is used to create all terrain by taking heightfield or procedural data as input and using it to displace the normally flat sphere of the planet.