To make these explanations simple.... I may have lied... a little!
(these explanations are intended for not scientists of course!)

Cardiovascular system = mostly, I mean the heart and the blood vessels.

cellular mechanisms = The entire body, and the brain are made up of "cells". These cells (including heart muscle and nerve cells) communicate with each other by chemical and electrical signals. Cellular mechanism means, here, the way individual cells send and receive signals.

Chemical stress factors = chemicals within the body (particularly the brain) which are released during stress. They signal information from one part of the brain to another. There are several released in the hypothalamus alone, such as neuroactive steroids, neuropeptides, catecholamines and imidazolines (explanation of these terms is a little out of the scope of this micro-glossary).

Hypertension = high blood pressure.

Hypothalamus = this is an area deep inside the brain which is largely responsible for controlling the production of hormones, but it has other functions to.

Medulla = An area of "lower" brain, i.e., just up from the spinal cord.

Nerve Cell = nerve.

Neural outputs = Any given nerves can send messages in only one direction, therefore, a "neural output" from the brain sends messages from the brain to some other part of the body.

Neurone = nerve, spelt "neuron" by Americans (typical!!).

Pathophysiological = When something is not working properly!.

Stress = In this context, stress means emotional stress (such as a fright) or physiological stress (such as injury or severe exercise) or a combination of both (such as waking up in the morning!).

Sympathetic pre-ganglionic neurones = Nerves in the spinal cord which pass nerve signals (messages) on, from the spine, to organs such as the heart and blood vessels. NB., in this context, "blood vessels" count as organs.  The sympathetic nervous system consists of all those nerves responsible for the "fight or flight" response.