"The elements of the natural world" - this is the subject of the sentence. "elements" is the head noun, and they are of the natural world, meaning trees, rocks, etc - things in nature.
"not only offer the raw materials for manipulation but also inspire the motivation to experiment and explore" - this is the predicate of the sentence, which tells you something about the subject above. "offer" and "inspire" are the main verbs. "not only" and "but also" means the subject both offers and inspires. More specifically, it's saying that people believe the subject offers, but the subject also inspires. What it offers is "raw materials" for "manipulation". What is inspires is the "motivation" to "experiment" and "explore".
So basically, the whole sentence is saying something like, "Trees, water, etc. are things(ingredients) you can use (for example, you can turn tree into paper), AND they are 'fun' things that make kids want to experiment and explore."