I recently decided to pick up Jared Diamond's excellent novel, Guns, Germs, and Steel (basically an account of the rise of human civilization) and I'm particularly interested in the influence of these eras on later societies, and how starkly different it is for both. I'm asking because despite it being a good novel, Diamond actually never goes out to explain the rigid difference between these two eras, but instead goes to explain the implications of a change from Paleolithic ways to Neolithic ways. Simply put, I'm curious on how both these ways of living have influenced us today, in ways we might not even be aware of.
So one quick thing, a lot of people in academia have some, uh, let's say strong feelings about that book, so take it with a grain of salt.
That being said, I think I can answer a few of your questions for you.
To start, the paleolithic means "old stone age" and Neolithic means "new stone age". Basically these were periods in time in which people used stone tools predominantly, little to no metal working at all. Also, the dates of these terms vary depending on the culture, and in some places they use different terms to describe this lifestyle.
As for how they effected modern life, look around you! Technology is not a tech tree, and by that I mean it's not like they were following a path. People used stone tools because they were cutting edge for the time, excuse the pun, and should be looked at as almost the iPhone of the time period, an everyday device that helped them go about there lives.
To sum up, to ask how these periods effect today is like asking how your second grade math class effected your English ACT score, we can't directly say, however, it was for sure a foundation for some idea at some point.