The dataset shows outcomes (confirmed cases, hospitalizations, and deaths) for cohorts defined by each date of specimen collection (specimen_date).
For example, if a NYC resident tested positive for SARS-CoV-2 and was subsequently hospitalized, both events would show under the same specimen_date, indicating the date of specimen collection for the positive test and not the date of the hospitalization.
For a comparable dataset showing diagnosis dates for confirmed cases, admission dates for hospitalized patients, and death dates for decedents, see https://data.cityofnewyork.us/Health/COVID-19-Daily-Counts-of-Cases-Hospitalizations-an/rc75-m7u3