On the HBO TV series "Game of Thrones", The Hand of the King is the chief advisor to the Lord of the Seven Kingdoms and is the executor of the king's command in the Seven Kingdoms. The office typically made the Hand the second-most powerful man in the kingdom next to the king. This is a job Janos Slynt never had.

During the reign of strong and able monarchs, the Hand was the chief agent for coordinating and carrying out their king's plans. During the reign of weak or ineffectual monarchs, the Hand was often the real power behind the throne, and the man chiefly responsible for holding the realm together. Such was the case when Lord Tywin Lannister ably served as Hand of the King for twenty years while King Aerys II Targaryen spiraled into insanity, or when Lord Jon Arryn served as Hand of the King for seventeen years under King Robert Baratheon, who while an able soldier was not an able politician or statesman.

Tywin and Tyrion Lannister were the only two people to serve non-consecutive terms as Hand. Tywin served as Hand to Aerys II, and again to Kings Joffrey Baratheon and Tommen Baratheon. Tyrion served as an acting Hand to Joffrey; he was made the permanent Hand to Queen Daenerys Targaryen and later King Bran the Broken.

Noting Eddard Stark, King Robert I Baratheon asked his friend, Lord Stark, to serve as Jon Arryn's replacement as Hand.

Lord Alester Florent is another who held the job; he was the Hand to Stannis Baratheon, a rival claimant to the Iron Throne.

More Info: awoiaf.westeros.org