Say you're a peasant, and anywhere between a third and a half of everyone you know has just died very quickly and in a pretty nasty way, apparently indiscriminately, at all levels of society. Life changes in a lot of ways, but specific to your question:

People's opinions varied, but in general, they thought the world was ending. When the plague died down and the world in fact hadn't ended, they were left with a deeply alienated feeling that a lot of people tried to escape with worldly pleasures. At least, that's the impression we get from some of the post-plague literature. Chaucer's Pardoner's Tale is a great example of this, which deals directly with the plague, and the Decameron is another one set during the plague.

As far as daily life and the next generation, the plague was arguably the beginning of the end of serfdom. When half the population died, the labor of the surviving half became a lot more valuable. There was some back and forth between the workers and landowners-- workers started demanding higher wages, the crown passed laws making it illegal to refuse work offers (read: ones that didn't pay well), everyone got much higher buying power, the crown passed Sumptuary Laws making it illegal to dress outside your social status, etc. In short, the upper class tried frantically to maintain the old social order, but the fact was that people were jumping into the new middle class faster than they could handle. The late 14th century is riddled with "peasant" revolts (there were actually a lot of non-peasants involved), and bit by bit, serfdom withered away. The generation that survived the plague was the very start of that. For more reading, check out the Jacquerie in France, the Great Rising in England, and the Bread and Cheese Revolt in Holland.