Maybe it would be better to start with a simple word, like good.
Good is an adjective. If we describe something as good, it has features of some kind that make it desirable. But what are those features? Well, it depends what the thing is. Good food is tasty, nutritious, etc. A good person does good things.
A feature is a noun: if we want a noun to describe a good feature, we put -ness on the end of an adjective, and we get goodness.
Penurious is an adjective: if a person has no money, we can say that he or she person is penurious. If we want to talk about the state of having no money, we need a noun: put -ness on the end, and penuriousness is that noun.
Adding -ness isn't always the right thing to do though: the word penury is a noun, and is changed to an adjective by adding the -ous ending to make penurious. So we don't need to adding -ness in this case- we can simply cut some letters off to get back to a noun (penury).