The Samaritan woman hears Jesus promise 'living water' while the two are sitting beside a deep well. Her response is practical: Jesus has no vessel with which to draw, and Jacob provided the well from which generations have drunk.
The misunderstanding works because 'living water' already had an ordinary meaning.
In biblical and Jewish usage, living water could refer to fresh, flowing water, especially water from a spring rather than stagnant stored water. Such water also had importance in purification contexts. At a deep well, obtaining water required a container and often a rope, so the woman's objection is entirely sensible.
Jesus shifts the image from physical water that must repeatedly be drawn to an inner spring 'springing up into everlasting life.'
The everyday meaning makes the metaphor stronger. Jesus starts with something the woman understands intimately—water, thirst, a deep ancestral well, and the labor of drawing—and uses it to describe a gift beyond what Jacob's well can provide.
The conversation thus moves from ordinary physical necessity to the life that comes from God without treating the woman's initial interpretation as irrational.