Why do we need Kelvin or 4 Wires operation?

In short, that’s because all interconnect has resistance, for sure some amount of voltage will drop across the cables, causing less than desire voltage level at load end.

Why 4 wires or kelvin operation is the solution? See the diagram below, since there’s no voltage drop across the sense wires, the source see what the actual voltage across the load, and can adjust accordingly.