fullcalendar

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.22.2/moment.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/fullcalendar/3.9.0/fullcalendar.min.js"></script>
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/fullcalendar/3.9.0/fullcalendar.min.css">
<div id='calendar'></div>

CSS

.day-highlight {
  background-color: yellow !important;
  color: red !important;
}

JavaScript

$(document).ready(function() {
  $('#calendar').fullCalendar({
    header: {
      left: 'prev,next today',
      center: 'title',
      right: 'month,agendaWeek,agendaDay'
    },
    dayClick: function (day){
      $(".day-highlight").removeClass("day-highlight");
      $(this).addClass("day-highlight");
    }
  });
});