您可以更改代码

function showMe(e) {
    var strdisplay = e.options[e.selectedIndex].value;
    var e = document.getElementById("idShowMe");
    if(strdisplay == "Hide") {
        e.style.display = "none";
    } else {
        e.style.display = "block";
    }
}

<select onchange="showMe(this);">
    <option>Hide</option>
    <option>Show</option>
</select>

<div id="idShowMe" style="display: none">
    <b>Hello world!</b>
</div>