Gain increasing amounts of AD or AP, Adaptive over the course of the game.
Fleet Footwork is a great AD Carry keystone for champions who can be abused by their short range, allowing them to sustain reliably into the late game.
Overheal synergizes well with Fleet Footwork, Bloodline, and Taste of Blood, keeping to topped off in lane.
Sivir's 3 item power-spike typically only includes 1 Attack Speed item so the extra bit from Alacrity lets you get in more of those hard hitting autos.
Cut Down is great for chopping down tanks, melee supports, and mid laners who might build Rylais and/or Liandries.
Sivir is the queen AD Carry of moving fast and Celerity further enhances that, synergizing well with your [R] and passive Movement Speed.
If there is one thing Sivir does better than any other AD Carry, that's clearing minion waves to stall out games. Gathering Storm empowers your ability to stall games into the late game and stack massive Attack Damage to take over a teamfight.