Vayne is a range ad carry that can serve as an assasin thanks to her burst damage and movility. Vayne shines during the late game thanks to her insame true dagame based on health %. She also has an invisible time to positionate. She is strong against any type of champions and can turn gamess around easily.

Every champ has is weaknesses and strong points.
If played Vayne correctly, she will hit like "A truck filled with trucks full of trucks" - Ocelote.
In teamfights she is one of, or maybe even the strongest.

Pros
+ Amazing kit to outplay.
+ With Ashe only ADC with stun.
+ Anti HP heavy tanks ( Silver Bolts).
+ Great escape tools.
+ Extremely good kit for 1v1.
+ Tumble is a great low cd steroid to your DPS.
+ Final Hour Is one of the best 1v1 ults for ADCS.
+ Every 3rd hit you deal greatly extra damage.
+ Can escape out tricky situations with Condemn and Tumble+ Final Hour.
+ You can rape the concentraction of your opponents with the stealth of Final Hour+ Tumble

Cons
- No skillshots like Mystic Shot(You can look at this as a pro and con, depends on the situation)
- Often gets earlygame denied by skillshot/high(er) range champs as Caitlyn and Ezreal
- Weak laning phase
- Squishy as hell
- Can be bursted down really easily
- Not a high attack speed in early.
- Easily to push her out of lane
- Succeeds mid/late, not early
- Heartseeker Vayne dumped Dr. Mundo :(
- Her Condemn stun can get denied by Flash or Arcane Shift