Classic example "Index in Books"
Consider a "Book" of 1000 pages, divided by 10 Chapters, each section with 100 pages.
Simple, huh?
Now, imagine you want to find a particular Chapter that contains a word "Alchemist". Without an index page, you have no other option than scanning through the entire book/Chapters. i.e: 1000 pages.
This analogy is known as "Full Table Scan" in database world.
But with an index page, you know where to go! And more, to lookup any particular Chapter that matters, you just need to look over the index page, again and again, every time. After finding the matching index you can efficiently jump to that chapter by skipping the rest.
But then, in addition to actual 1000 pages, you will need another ~10 pages to show the indices, so totally 1010 pages.
Thus, the index is a separate section that stores values of indexed column + pointer to the indexed row in a sorted order for efficient look-ups.
Things are simple in schools, isn't it? :P