I understand these words, but not in the combination used.

I guess this is really simple to people with the nessecary maths background to understand this, but for me I just don't see the connection between vectors/gradients and type systems.

I don't think there is any connection. But since the submission was titled "covariant and contravariant" without any kind of context, it seemed appropriate that we could all share our own personal ideas about what these words were supposed to mean.

Ok. the source of the confusion for me then was that I was not previously aware that covariant and contravariant were terms that could be applied to vectors.