The word "palpable" means "able to be felt." In other words, if something is palpable, you can actually feel it in a physical way. The word can also be used more figuratively. We can say that some emotional feeling is so strong that it is "palpable." In such a case, we do not mean that we can literally feel it, but that it is so strong as to be easily perceived by the mind.
In The Giver, the word is used in this figurative way. Jonas remembers how terrified he was when the airplane flew over. He thinks that it was such an intense terror that it was palpable. In other words, it was so strong that he could easily perceive it in his mind.