Tyrosh is one of the Free Cities located to the east of Westeros. It is situated on an island off the southwestern coast of Essos, in the Narrow Sea. It is located at the eastern end of the Stepstones, an island chain that extends from Essos to Westeros, which according to legend used to be a land-bridge linking the two continents. Therefore, Tyrosh is the closest of the Free Cities to Westeros, located not far from Dorne and the Stormlands (fairly close to the island of Tarth).
Due to its central location - between Westeros and the other Free Cities, at the middle latitude of the Free Cities between Braavos in the north and Volantis to the south, and its proximity to constant wars between Lys and Myr in the Disputed Lands - Tyrosh is often seen as a major world hub for hiring the services of various professional mercenary companies, to serve in the various conflicts of these different regions.
In the books
In the A Song of Ice and Fire novels, Tyrosh is one of the most powerful of the Free Cities. It is said to dwarf Sunspear in size. It is reported to be boisterous and loud, with a large harbor guarded by the Bleeding Tower.
The people of Tyrosh are called Tyroshi. They love loud and garish colors. They are known for their creation of ornate armor and elaborate torture devices. Pear brandy is an export of the city. Slaves and mercenaries are commonly hired there.
Tyrosh has a volatile history. Like most of the Free Cities, it was once a colony of Valyria. Following the Doom, it became an independent city-state. However, a century later it was attacked by Volantis, which was trying to reforge the Valyrian Freehold. Having already taken Myr and Lys, Volantis overreached by attacking Tyrosh. Pentos and the Storm King in Westeros allied with Tyrosh to defeat Volantis, which also lost Myr and Lys due to rebellions and uprisings.
Two and a half centuries later, Tyrosh was attacked and captured by the Band of Nine, nine powerful warlords who were supporting one another in doing together what could not be achieved alone. Alequo Adarys was installed as Archon of Tyrosh. The Band's military strength was broken in the War of the Ninepenny Kings, when the King on the Iron Throne, Aegon V Targaryen, launched a pre-emptive strike before they could attack King's Landing. Adarys managed to retain control of Tyrosh for six years before being deposed. Hoster Tully, the father of Petyr Baelish and the young Barristan Selmy all fought in the War of the Ninepenny Kings, Selmy winning fame for his slaying of Maelys the Monstrous, the last of the Blackfyre Pretenders, in combat.
According to the TV series official pronunciation guide developed for the cast and crew, "Tyroshi" is pronounced "Ti-ROH-shee". "Tyrosh" is pronounced "Ti-ROHsh", as opposed to "Tie-rosh".