Hormuz is located on the Straits of Hormuz, the narrows at the mouth of the Persian Gulf. The Straits have been mentioned fairly often in news over the last few decades because of their strategic importance. They are the best place to control traffic in or out of the Gulf; if someone wanted to cut off seaborne shipments of something — Gulf oil going out, arms coming to Iran, or supplies to US forces in Iraq — this is where they would do it.
In medieval times, Hormuz was the capital of its province and the province is still called Hormozgān, though the city of Bandar Abbas is now the capital. To escape Mongol attacks, one ruler shifted the capital to nearby Hormuz Island and built a town there called New Hormuz, but he soon made peace with the Mongols and moved the capital back.