The New Adult age range is began fairly recently and isn't accepted by all publishers or bookstores. It tends to be most common in romance genres and may be classified as young adult or adult in other genres. But those who use the term all agree on their definition.
New Adult books are intended for 18-25-year-olds. The main character of a new adult novel should fall within the same age range as the intended readers, but more than that, they need to be experiencing adulthood as something new and confusing. That is what differentiates these books from the more general adult audiences.
The stories in new adult novels are about college, first jobs, leaving home, and other new and overwhelming life experiences that happen during early adulthood. Adulting, responsibility, independence, self-sufficiency, and similar themes make up the books in this age range.
As books intended for adults, there tend not to be any strict content standards about violence, drugs, graphic content, etc. As the next step from YA novels for many readers, the themes can be darker and the romances steamier now that the characters are adults.
Like general adult books, you will need to use your genre to determine the best word count, but I've seen about 60,000-85,000 words recommended.