Here are the basics: The show takes place in a country called Westeros, also referred to as the Seven Kingdoms. The main conflict of the show is the battle among various groups and families for the right to rule Westeros. King Robert Baratheon fought a war against the current king and won, earning the right to rule the country. However, he died in what was believed to be a hunting accident. The succession seemed assured because of his oldest son, Joffrey, but it's soon discovered that Joffrey is actually the product of an incestuous relationship between the queen, Cersei, and her brother Jaime. Joffrey is crowned nonetheless (the Lannisters insist the incest is only rumor) and currently rules as king of Westeros, but many believe he does not have the right to be king because he is not Robert's son, and other factions are currently fighting to take control of the throne.
A character you'll hear about but never see is Eddard "Ned" Stark. An old war comrade of Robert's, Ned was selected by Robert to hold the prestigious position of Hand of the King – the monarch's most valued advisor and the one who can make decisions as a representative of the king or queen. However, due to Queen Cersei's machinations, Ned was executed for treason in season one after he discovered the truth about Joffrey's parentage.