Attunement does a few things, it adds extra memory slots so you can equip more spells, it increases the amount of casts for each equipped spell, it increases spell casting speed, and 3 points of attunement = 1 point of adaptability for the purposes of raising agility (which increases dodge i-frames and estus drinking speed). 10 for the first memory slot, 13 for the 2nd, 16 for the 3rd, 20 for the 4th, 25 for the 5th, etc.
Even if you don't plan to raise Intelligence or Faith to do spells / hexes/ miracles it's nice to have some memory slots to use pyromancy as it mainly scales with the power of the flame which just costs fire seeds and souls to upgrade. Even if just for Flash Sweat which greatly reduces fire damage or Warmth which can be used to heal NPC summons. There's also a ring and a hat which can add extra attunement slots. You probably already have the ring, the Southern Ritual Band, as you get it after killing the Gargoyles.