An author's style is their voice.
It's how they're recognized ... it's how they express the thoughts presented in the book.
Think about your own VERBAL voice.
Do you speak at the exact same tone and articulation as your friends, or do you all sound different? Surely, you've heard people speak in different accents, right?
Likewise, when writing, something YOU write would likely be expressed differently by someone else. Give it a try. Pick a topic sentence, and based on singularily that, have both yourself and another person write an entire paragraph having to do with it. Afterwards, compare the paragraphs. How are they different? How are they similar?
Sorry, maybe I'm not making this any clearer ... like you said, this is difficult to explain. Some authors use more dialogue than description; some authors drone on, while others are more to-the-point. Some authors have a vast vocabulary, while others are quite simple.
Maybe this will help -- go pick out two books written by different authors. Describe how the writing style is different. It's tough, I know, but give it your best shot.
Good luck, and I hope this helped. :}