Gain 3% extra MS. Gain extra AP or AD, based on your bonus MS, Adaptive.
Singed's unique play-style allows him to excel in situations where he is able to cheese and split-push. Spellbook allows him to not only cheese for a kill by taking ignite, but also gives him the freedom to use his Summoner Spells more liberally thanks to the bonus Summoner CDR.
Singed likes to run, and if you're able to effectively make it to the 10min mark without boots you'll be running even faster with the enhanced boots.
Biscuit Delivery not only grants a massive amount Health regeneration but mana as well. Combined with the Inspiration's +20% potion bonus and Dark Seal, you can easily double the strength of all potions and Biscuits.
Cosmic Insight doubles down on even more Summoner Spell cooldown keeping you extra safe and allowing you to keep up lane pressure with Ignite and spam.
WhyThe Ultimate Hat
The Ultimate Hat's ability to keep your [R] on a short cooldown keeps you extra safe when paired with your extra short Summoner cooldowns.
Naturally Singed relies heavily on Movement Speed and the extra bit from Celerity help you to run circles around your opponent.
Celery also grants your [R] a little bit of extra Ability Power when on the move.