The best way to think of Rainbow Six Vegas is as a whole new ball game for the series as this in many ways is actually serving as a reboot of the series. Ubisoft had a clear vision for what they wanted Rainbow Six to be going forward.
As you would expect the story is set in Vegas one of the tourist hot spots of the world. The basics of the story are that Las Vegas is going to be hit with one of the worst terrorist attacks of all time and only Rainbow team can stop it. One of the interesting things about the story is that you experience the majority of it in game and not with lengthy cut scenes. It actually works very well and immerses you in the action.
Gameplay wise, Ubisoft really changed things up as Rainbow Six Vegas feels like no other Rainbow Six game. While you could still give orders to your teammates (which you did with the d pad) things like regenerating health, 3rd person cover shooter sections and the fact that missions had checkpoints gave the game a much more action packed feel than any other game in the series. One of the coolest things they added was using ropes to move up and down the building all the while shooting! Gameplay was nice and tight and for many was that perfect blend of being action packed while also offering tactical based gameplay.
Rainbow Six Vegas was a huge hit. It was very well received, people love the single player campaign and multiplayer was very popular as well. In all, it was a great reboot of the series and actually introduced many new players to the series as well.