@myVariable is a server-side variable it get's it's value from server before rendering the page
@myVariable will print the value of the variable not assign to it,
so the output of @myVariable = true; will be 
false = true;
use ajax to get content from server
@{
    bool myVariable = false;
}
<script type="text/javascript">
    function Foo() {
       if (some_condition)
       {
          $('#newContent').load('/News/GetLatest/10'); // call ajax to get content
       }
    }
</script>
   <div id="newContent">
      <!-- stuff -->
   </div>
or you can only show the div if condition is true on the client side
@{
    bool myVariable = false;
}
<script type="text/javascript">
    var showContent = @myVariable; // false
    function Foo() {
       if (some_condition)
       {
          showContent = true;
          $('#newContent').show(); // show it
       }
    }
</script>
   <div id="newContent" style="display: none;"> <!-- hidden by default -->
      <!-- stuff -->
   </div>