Despite its name, the East River is not a true river. It is a tidal estuary (more precisely, a drowned valley / tidal strait) connecting two large bodies of water: Upper New York Bay (south) and Long Island Sound (north).
It's crossed by 9 bridges (Brooklyn, Manhattan, Williamsburg, Queensboro/59th St, RFK/Triboro, Bronx-Whitestone, Throgs Neck) and 4 tunnels (subway, road, water).
Once severely polluted, water quality has dramatically improved. Now supports striped bass, bluefish, oysters (restoration), seals. Popular for kayaking (NYC Water Trail), ferry commuting (NYC Ferry), and riverside parks (Brooklyn Bridge Park, East River Esplanade, Roosevelt Island).
Early European settlers (Dutch/English) named it a "river" because it appeared as a flowing freshwater stream at low tide. The name stuck. Geologically, it's a fjord-like estuary carved by glaciers, flooded by rising seas.