Placing bookshelves near your enchantment table will allow you to use higher level enchantments. Bookshelves in any of these positions can contribute to the maximum enchantment level, as long as there is empty space between the table and the books:

There are 32 positions that the code checks for bookshelves, but the bonus for having bookshelves is capped at 15. With 15 bookshelves in range, the maximum level you can reach is 30.