Visualise normal and visualise tex coords are shaders which give an RGB representation of the 3D vector (the surface normal or the texture coordinates). The R value of the colour is the X component, G is Y, and B is Z. Surface normal values which range from -1 to +1 are remapped into the visible range 0 to 1.
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.