I did (developmentally appropriate, activity embedded) behavioral intervention with children with disabilities for a few years.

I know this info is likely in your chapter, but it made more sense to me as a diagram...I had a 2x2 grid pictured in my head, each quarter labeled:
Positive=giving something
Negative=taking something
Reinforcement=increases the likelihood a behavior will be repeated
Punishment=decreases the likelihood a behavior will be repeated

So negative reinforcement means removal of an aversive stimulus, and the removal reinforces the behavior. Real life example: If a child is wearing itchy socks and verbalizes "Socks off," the removal of the itchy socks negatively reinforces use of the language to get the need met, so that the child is more likely to say "Socks off" the next time they do not like the feel of their socks.