What are dragon-shouts? Well, well since your character is Dragonborn he is one of the few people who can speak draconic, and those words have special powers. Silvade can explain it better.
:P
Dragon Shouts are special abilities that you get in game by completing tasks, quests and things like that. There are over 20 different shouts, each one casts a unique and powerful spell, it's very likely that they will work like greater spells and be available for use only one time a day.
The player as being one of the Dragonborns, has knowledge on Dragonic, an ancient language used by Dragons. By shouting three or more specific words he will be able to execute this spell-like ability and summon dragons, or slow time, knock foes in a certain radius, etc.
The only thing, I think, it relates to VATS, is that it's probably going to be a separated button/key from the spell. One (Two in case of dual spells) will be for casting a common spell, the other will be for shouting. Just like spells, it will probably be selected on the Magic menu.