Jquery ajax post request not working

According to jQuery documentation, you must declare the data type:

$.ajax({
  type: 'POST',
  url: url,
  data: data,
  success: success,
  dataType: dataType
});

Also, looking at your server-side code, you don't actually want to post JSON formatted data. This {"post-form":postcontent} is JSON formatted data. What you actually want to do is send TEXT or HTML. Seeming as it's form data, I would guess at TEXT.

Try this:

$.ajax({
   url: '/post',
   type: 'POST',
   data: 'post-form='+postcontent,
   dataType: 'text',
   success: function(response, textStatus, jqXHR) {
     alert("Yay!");
   },
   error: function(jqXHR, textStatus, errorThrown){
     alert(textStatus, errorThrown);
  }
});

Since you are posting JSON-data you have to declare the dataType "JSON":

$.ajax({
  url: '/post',
  type: 'POST',
  dataType: "json",
  data: {"post-form": postcontent},
  success: function(response, textStatus, jqXHR) {
    alert("Yay!");
  },
  error: function(jqXHR, textStatus, errorThrown){
    alert(textStatus, errorThrown);
  }