The Esquiline was the largest of the 7 hills of Rome. Its claim to fame comes from the Roman emperor Nero who built his domus aurea 'golden house' upon it. Before the Empire, the eastern end of the Esquiline was used for dumping refuse and the puticuli (burial pits) of the poor. Carcasses of criminals executed by the Esquiline gate were left to the birds. Burial was forbidden within the city proper, but the burial area of the Esquiline was outside the city walls. For health reasons, Augustus, the first Roman emperor, had the burial pits covered over with soil to create a park called the Horti Maecenatis 'Gardens of Maecenas'.
The Colossus, Temple of Claudius, and Baths of Trajan were all located on the Esquiline.
Mary Beard, classicist and columnist for the UK Times, lists the following 10 hills of Rome: the Palatine, Aventine, Capitoline, Janiculan, Quirinal, Viminal, Esquiline, Caelian, Pincian, and Vatican. She says it is not obvious which should be counted as the 7 hills of Rome. My list is a standard one, but she does, or course, have a point.