The ancient Romans borrowed a great many ideas from other ancient civilizations. One of those ideas was the chariot, an idea they probably borrowed from the ancient Etruscans. Most travel in ancient Rome was by cart pulled by oxen, by walking, or by boat. Chariots were used for travel on the Roman roads when there was no need to carry a lot of weight. Chariots were sometimes used by the military.
But the real use of chariots in ancient Rome was for racing. When Rome was a kingdom, young Roman men raced each other on chariots around the seven hills, causing destruction to property and danger to pedestrians. Rome was not built as a racetrack. So of course there were problems. Under the Republic, racing continued but because of new laws harm to property and person could become a court case if things were not settled out of court. Under the Empire, chariot racing was much better controlled. There were race tracks all over the Empire. These race tracks were called circuses. The best chariot racing in the Empire was held at the Circus Maximum in the city of Rome.
Admission to events in the Circus Maximus was free. Men, women, kids, slaves - anybody could attend. People cheered for their favorite rider or team. Winning chariot riders were treated like movie stars or rock stars are today. It was a very dangerous sport. Many riders died seeking glory in the Circus Maximus.