How to use date variable in sql developer's "Enter Binds" dialog?

Try changing your query to be:

select first_name,
       last_name,
       dob,
       org
  from emp
 where dob > to_date(:highDate,'DD-MON-YYYY');

then when prompted, enter '20-JAN-2010'.

Just copying the answer from Oracle Community forum:

You should be able to enter dates which conform to your NLS_DATE_FORMAT setting.

e.g. If NLS_DATE_FORMAT is DD-MON-YYYY, you can enter 24-jan-2011 for today's date.

Worked for me.

Try using a substitution variable. For example:

select (&var - 1) from dual;

sql developer will ask you to enter a substitution variable value, which you can use a date value (such as sysdate or to_date('20140328', 'YYYYMMDD') or whatever date you wish).