Documentation for JIRA 4.2. Documentation for other versions of JIRA is available too. 

When you are not in edit mode, the examples in the rightmost column show you how the various formats will appear.
To set the date picker format, see 'Advanced JIRA configuration with jira-application.properties'. Here are some example configurations for U.S time:
| Preferred Date | Configuration in jira-application.properties | 
|---|---|
| Oct/1/10 |  jira.date.picker.java.format = MMM/d/yy  | 
| 10/05/10 |  jira.date.picker.java.format = MM/dd/yy  | 
| Jan 5, 2010 |  jira.date.picker.java.format = MMM dd, yyyy  | 
| 10/05/2010 |  jira.date.picker.java.format = MM/dd/yyyy  |