With its back to the East River and Brooklyn, the amphitheater --- sometimes referred to as a bandshell --- offers theater, dance and music events. The wooden bench seating is not covered.
The New York City Department of Parks & Recreation site details the history of the amphitheater:
"In 1941, an amphitheater was built in the park, along with an adjacent limestone recreational building, as part of an urban renewal project for the Lower East Side. Joseph Papp (1921-1991), founder of Shakespeare in the Park and the Public Theater, staged Julius Caesar there in 1956. During the 1950’s, the amphitheater was the site of frequent free Evening-in-the-Park concerts. Local schools held their graduation ceremonies there, and the Group of Ancient Drama performed the Greek classics (gratis). In 1973, however, the amphitheater closed due to budget cuts. Vandals attacked the neglected theater and by 1980 it was unusable."
The amphitheater was restored by the city after September 11, 2001, as part of the efforts to revitalize Lower Manhattan.