Try this:
$.each(Months,function(i){
item_html += '<option>'+Months[i]+'</option>';
});
instead of
$.each(Months,function(i){
item_html += '<option>'+Months+'</option>';
});
Another thing is your JSON item
is an array object.
item =[{"Title":"DataTitle","Months":"January,February","Location":"Africa"}];
item_html ="";
item_html += '<h3>'+item[0].Title+'</h3>';
if(item[0].Months.length !== 0) {
var Months = item[0].Months.split(",");
item_html += '<select>';
$.each(Months,function(i){
item_html += '<option>'+ Months[i] +'</option>';
});
//or
//$.each(Months,function(i, month){
// item_html += '<option>'+ month +'</option>';
//});
item_html += '</select>';
}
item_html += '<h3>'+item[0].Location+'</h3>';
$('.displayarea').append(item_html).slideDown();
Here is the Demo