一息にいいますと、絞り込めるようになるってことです。

interface Interface01 {
  type: "Interface01";
  Interface01: number;
}

interface Interface02 {
  type: "Interface02";
  Interface02: number;
}

type InterfaceUnion = Interface01 | Interface02;

function interfaceSearch(arg: InterfaceUnion) {
  let typeNumber: number;
  switch (arg.type) {
    case "Interface01":
      typeNumber = arg.Interface01;
      break;
    case "Interface02":
      typeNumber = arg.Interface02;
  }
  console.log("Interface01: " + typeNumber);
}

interfaceSearch({ type: "Interface01", Interface01: 10 });