I don't have cable or satellite so I have never seen the show Game of Thrones.
It is a great American Fantasy series created by David Benioff and D.B. Weiss. I hope you have a chance to see it someday.
What is the storyline?
It is set on the fictional continents of Westeros and Essos. It has many plots but centers on three primary story arcs.
Does it have battles, and when is the time in which it is set?
It does have battles. In the first arc, the Iron Throne of the Seven Kingdoms people vying to claim the throne or fighting for independence from the throne.
It sounds like it's full of action.  I can understand why so many people love it.
It has been running a long time. It will conclude it's eighth season premiering in 2019.