Do bookshelves around an enchantment table make the enchantments better?

Yes. The wiki has an in-depth article on the mechanics, but the very essence is that bookshelves placed within a 5x5 ring centered on the table, on the same level as the table and 1 level above contribute to the enchant level. Up to 15 bookshelves matter. Their distribution within that ring doesn't matter; what matters is that there's nothing between them and the table (within the 3x3, 2 tall ring around the table) - only air; no torches, no tall grass, no snow layers, no carpets etc.

The effect of adding the bookshelves is apparent as the cost of enchantment (in levels) increases - once your bottom slot enchantment requires you to have 30 levels, you have maxed out the enchanting setup.

Note this is still random - probabilities change, but you can still occasionally get scrub enchantments in max tier setup. Also, some basic, simple but useful enchantments are phased out and replaced by high-level low-usefulness enchants like Impaling V or Bane of Anthropods IV.

Yes, in short, at 15 bookshelves the enchantment table "maxes out" and unlocks the level 30 enchantments that are what you should be aiming for. The positioning is the enchantment table in the middle, a 3x3 ring of nothing, then the 15 bookshelves somewhere in the 5x5 surrounding the 3x3.

But yeah it does make it pretty. I highly recommend doing this with every enchanting table you will use.