Tuple's really don't have a lot to do with functional programming, they are a common concept in many language that for some reason are only making their way in the .Net on version 4.0. One could argue that you could have always easily constructed your own Tuple class but unnecessary duplication of such a simple type has obviously become apparent to the BCL team. This is good. Simple classes like this should be present in the framework. :)
So what is a Tuple? It is basically a container of a finite list of objects; a Point could be described as a list of 2 values Tuple<int, int> where the int values could be the X and The Y coordinates of a point. A Date could be described as Turple<int,int,int> with the values being Year, Month & Day. It is not a list in that your would typically enumerate through the items but you would reference them by index. You may be ask why is this different to an Array eg int[3]? Well with a Tuple the list length is set at compile time and the type of each index point is also set. Tuple<int,string,DateTime> forces you to always have the DateTime as the 3rd item. This is all pretty under-whelming to be honest, but like anything cool its the simplicity that is its strength and also why it pops up in functional styled programming a lot. Future demos are likely to include Tuples :)