Gain increasing amounts of AD or AP, Adaptive over the course of the game.
+9% Attack Speed
+6 AD or 10 AP
Kleptomancy procs exactly like Sheen resulting in Ezreal being one of the biggest abusers of the proc though the use of [Q].
The consistent influx of both Mana and Health potions saves you a lot of money over the course of the game paired with a significant income from the occasional "Sacks of Gold" proc.
Magical Footwear combined with Klepto is designed to skyrocket you ahead in item efficiency for an extremely powerful mid-game.
Klepto potions plus Biscuits means you shouldn't have to purchase many potions at all with earned gold. The extra bit of maximum mana and mana sustain is also important for dishing out damage.
Ezreal probably loves CDR more than any other AD Carry does. CDR means more survivability and way more damage. The slight Summoner cooldown also provides safety in your weak early game.
If you're looking to build Iceborn Gauntlet instead of Tri-Force then Approach velocity is an interesting choice here to further chase down your target.
Manaflow band grants massive early game lane sustain when paired with the potions from Klepto. In the later points of the game when you have a stacked tear, Manaflow will refund massive amounts of mana.
Gathering Storm is your late-game insurance policy. Since you'll be spending the majority of your early game surviving and poking with [Q], the early damage isn't as necessary.