Twisted Pair Certification Parameters: NVP, NEXT, RL, IL, and the rest: What do they mean and what impact do they have

Each time we run a certification test on an installed link, we get many different parameters reported. But what does each parameter mean, and how does it influence transmission of signal over the cable?

What can we learn from each parameter? How do we identify and troubleshoot the source of particular failure types such as NEXT and RL?