A game resembling bagatelle, played on a special oblong board or table with a curved upper end, a set of numbered compartments at the lower end, side alleys, and the surface studded with pins and sometimes furnished with numbered depressions or cups.
"The children gathered around the old wooden tivoli to take turns rolling their balls down the curved table toward the numbered compartments."
In plain English: A tivoli is an old-fashioned amusement park that usually features rides and games for children to enjoy.
"We spent our summer vacation riding the Ferris wheel at Tivoli Gardens in Copenhagen."
An ancient city in the province of Rome, Lazio, Italy.
"The ruins of Tivoli stand as a testament to its history as an ancient city in the province of Rome."
The word comes directly from the Italian name of a town near Rome, which itself was derived from the ancient Latin city of Tibur. It entered English as a proper noun referring to that specific location and its famous gardens.