This is a great question, and I am sure many Japanese learners are confused.
Here is my opinion.
い adjectives are basic structures of adjectives in Japanese. When you write them with kanjis and hiragana, い adjectives tend to have both kanjis and hiraganas, which the hiragana part is called okurigana but you do not have to memorize the term. If you know kun yomi and on yomi, it is more easy to explain. The kanjis used in い adjectives usually have kun yomi.
And grammatically, い parts can be conjugated. For example, the negation of 美しい(utsukusii, beautiful) will be 美しくない.
On the other hand, the structure of な adjectives are different. Most of な adjectives can function as nouns without な. For example, 綺麗(kirei, beautiful)な, 素敵(suteki, great)な and 巨大(kyodai, enormous)な can function as nouns without な. 綺麗 is a noun that expresses a beautiful condition. 素敵 and 巨大 are same as this. They are nouns to illustrate certain conditions. If an adjective word can stand by itself without な part, it is a な adjective. Except な parts, な adjectives cannot be conjugated. The word きれい(kirei) ends with い, but this is an example of a な adjective. The negation of this word will be きれいではない. If I apply the conjugation of い adjective to きれい, it is going to be きれくない; however this is grammatically incorrect.
I hope this explanation helps you.