What is the difference between a point transformation and a vector transformation? This is what my lecturer told me in the coursework:

We only consider 4*4 matrices. These are used to rotate, scale or translate objects (or any combination of these operations). Matrices are also used later in the implementation of the virtual camera model. If you do not know the difference between a vector transformation and point transformation, look it up. 

I can't seem to find an answer and made an account for this website just for this question.
Here's the simple answer.

In 4D, to be able to multiply them by a 4x4 matrix, vectors are represented as (x,y,z,0) and points are represented as (x,y,z,1).

Since the 4th row of a 4x4 matrix represents the translation of the matrix, the above representations make it so points are affected by translation, but vectors are not.

Both vectors and points are affected by the rotation, scaling, etc though.

Caveat:

There is deeper discussion to be had if you expect the vectors to have certain properties.  For instance, if you transform a triangle's normal by the same matrix you transform the triangle's vertices, it likely won't actually be the normal vector of that triangle anymore. This is because normal vectors have a sort of inverse relationship to the vertices that they are calculated from.