1) Replacing DIV text from Resources File.resx
You can easily use a key from the Resource file in your DIV element by using <%$Resources:ResourceFile Name,Resource Key%>
.
In your case, you should use asp:Literal
control to display a text from Resource File (resx) as below
<div id="divID" style="display:none">
<asp:Literal runat="server" Text="<%$Resources:ResourceFile,Key%>" />
</div>
2) Replacing DIV content from Resources File.resx using JavaScript
The above solution will embed the resource entry to your code. However, if you need to set the DIV content with a Resource using JavaScript, you can use the below code:
document.getElementById("divID").innerHTML = '<asp:Literal runat="server" Text="<%$Resources:ResourceFile,Key%>" />';
Make sure the resource file name is correct and already provided the correct resource entry key.