The Idea behind this vayne build is to put more focus on casting and less on classic autohitting. By getting very much CdR and some nice onhit bonuses, wich fit the playstyle, you can go more the hyper style, vayne is supposed to be played.
So with much CdR and a Trinity, you can deal very high amounts of damage in a very short amount of time without losing damage potential very fast.

This style makes it easyer for the player to place in certain situations. 1v(<4) shouldn't do any problems, as long as you are prepared to fight.
As long, as your team is able to protect you from beeing bursted instantly, the teamfights are an 'easy to go' part of the game.

The pros of this build are, that it can be used on toplane and as well on botlane. Even the enemy team can do pretty much without you becoming useless.
The Idea is to have a very high dps over a long time so you can, as described in the item section, play against tanks and against dmg dealers.

Pros:
-high and lasting amount of dps
-very high chase potential
-high burst
-strong adc alround counter

Cons:
-still can get bursted
-no shield (banshees; Guardian Angel)
-mana expensive