  That information could be supplied by a huge catalog that specifies the spatial or temporal distance between every pair of events along every curve connecting them. Such a huge catalog would be massively redundant, however. If we know the distance from A to B and from B to C along some curve, then we know the distance from A to C as well. The minimum information we need is the temporal and spatial distance between each event and all those (loosely speaking) infinitesimally close to it. That information is what the metric field provides. It is a “field” since that information belongs just to one event. We can then piece together temporal and spatial distance along any curve just by summing all the distances between successive infinitesimally close points along the curve.