The rediscovery of this work caused a "swerve" in people's mental models. It forced people to change how they thought, what was possible and spurred the Renaissance (pursuit of beauty, happiness and truth)
Humans should conquer their fears and realize that everything transitory
Epicurus - Peace of mind is key to enjoying pleasure, pleasure should be your main goal and atoms are the building blocks of life
Christianity sought to censure Epicurean seeking of pleasure as they taught that pleasure leads to temptation. Epicurus also thought that if there were gods they only cared for themselves, that the soul is mortal, and he was skeptical as to why humans should be better/above any other animal.
Lucretius - Nothing is created with an end goal, things evolve out of necessity and over time adapt to their current functions. Humans are not special as we are made of the same thing as everything else; soul dies with the body; there is no afterlife; this world is all we have; religions are cruel; greatest obstacle to pleasure is not pain but delusion; inordinate desire destroy more lives than anything else; humans, while finite, have infinite imagination (for both pleasure and pain). Understanding how things really are is no cause for despair but rather the good news.
"To philosophize is to learn to die" - Montaigne
What I got out of it:
Definitely an interesting read but I can't say that I loved it or would want to read it again. However, it is interesting to contemplate what the Renaissance would have looked like, if it happened at all, without Poggio finding Lucretius' work. Also, it is interesting to ponder what treasures have been destroyed or are still left to be found that can impact our thinking as much as "On the Nature of Things" did.
There has been a lot of criticism around the accuracy of this book - especially many of the religious aspects. A great article summarizing these criticisms can be found here.