The term affordance refers to the perceived and actual properties of a thing. For instance, a chair is for sitting and glass windows are transparent and breakable. Affordances provide strong clues to the operations of things, and when they are taken advantage of, users needn't have to read the instruction manual at all. There are over 20,000 everyday objects. It is important that they are simple to learn and use. Designers should take advantage of the psychology of people with the knowledge of how things work.
The other important design principle is having a good conceptual model -- it allows users to predict the effects of their actions. Incorrect conceptual models will mislead users. People form mental models through experience, training, and instruction. When instructions are unclear or confusing, then users won't even bother to take advantage of all those features. Thus, all those features the designers put in are "wasted."
Mapping is the technical term that refers to the relationship between two things. With respect to the article, it means between the controls and how it affects the real world. Mapping problems are abundant and are one of the fundamental causes of difficulties.
A device is easy to use when there is visibility to the set of possible actions, where the controls and displays exploit natural mappings. Good design takes care, planning, thought, and conscious attention to the needs of the user.
Feedback is sending back to the user, the information about what action has actually been done and what it accomplished. Modern telephone systems are difficult to learn because they systems have more features and less feedback. Implementing something like a display screen would increase cost, so there is a trade-off between cost and usability.
The paradox of technology is that it should make life easier and more enjoyable, it also adds extra functions and increases complexity. However, this should never be used as an excuse for poor design.