Documentation for JIRA 5.1.x. Documentation for other versions of JIRA is available too. 

Please note that adding Javascript to custom fields is a customisation and not maintained as a supported part of JIRA.
In Atlassian's support JIRA, when a user creates an issue with "Critical" priority, it will display the "Priority Explanation" field.
This can be achieved by performing the following steps:
<script type="text/javascript">
  priority = document.getElementById('priority');
  if (priority) {
      target = document.getElementById('customfield_10000');
      // Hide the target field if priority isn't critical
      if (priority.value != 2) target.style.display='none';
 
      priority.onchange=function() {
          if (this.value == 2) {              
                     target.style.display = '';  
                     target.value="enter message here";
                  } else {
                 target.style.display='none';
          }
      }
  }
 </script>