Eridanus's own article calls it a river identified with the Po or the Nile. What that leaves out is why a long, winding river sits where it does, among a whole cluster of constellations sharing no plane or boundary but a single theme: water.
This part of the sky, running from Orion's foot down through Cetus, Piscis Austrinus, Delphinus, Equuleus and, before its eighteenth-century division, Argo, is old enough that the theme predates Greek myth-making. Babylonian sky-lore, which Greek astronomers inherited along with the zodiac itself, already read this stretch as a sea, because the Sun crossed it during the rainy season of the ancient Near East; the Greek figures were laid onto existing water imagery rather than invented over empty sky.
Modern astronomy calls this loose cluster the Heavenly Waters, a name used by historians such as Richard Hinckley Allen rather than a boundary Ptolemy himself drew, since his forty-eight were grouped only into zodiacal, northern and southern lists. Eridanus is one of the clearest members: threading among several other constellations exactly as a river should, it is the only figure in the group that is literally shaped like the thing it represents rather than merely themed to match.
Its brightest star, Achernar, marks the river's end deep in the southern sky, a fitting final point for the longest thread in an ancient sea that Ptolemy catalogued but did not invent.