3 potions: They are just for the start to get some life if you are missing too much.

Berserker's Greaves: Give Yi some attack speed (25%) and movement speed (enchance by 2) that he really need and that other boots can't give.

Phantom Dancer: That give attack speed (55%),critical strike chance (30%) and movement speed (15%) Because Master Yi need Those skill especially AS and MS.

Nashor's Thoot: Give ability power (65), attack speed (50%), mana regenaration (10%), cooldown reduction (25%) Ability Power is for Alpha Strike that do magic damage cooldown reduction is really usefull it reduce all his attack cooldown.

Malady: Give ability power (25%), attack speed (50%) and every physical attack you do reduce the target magic resistance by 6% for 8 seconds (stack up to 4 times) That give Yi more AS and AP and the alpha strike damage are increased.

The Black Cleaver: Give attack damage (55), attack speed (30%) and reduce by 15% for 5 seconds your target armor (stack up 3 times) That make Yi physical attack better.

Infinity Edge: give attack damage (80), critical strike chance (25%) and critical strike damage (50%) that boost again Yi physical attack

I Could suggest you to change the Black Cleaver for a bloodthirster when you have all done the
build.