The syntax should be as follows:
DELIMITER $$ /* if you're not using an editor, you must change the delimiter*/
CREATE
TRIGGER ai_jos_dhruprofile_each
AFTER INSERT
ON jos_dhruprofile
FOR EACH ROW
BEGIN
UPDATE jos_users
SET jos_users.department = NEW.department
WHERE jos_users.id = NEW.uid; /*<<<--- ; after every stament */
END $$ /* changed delimiter after the end */
DELIMITER ; /*make sure you set the delimiter back to the default*/
Note on the naming scheme for triggers
I'd recommend naming your trigger ai (meaning after insert) so you know when it fires on which table, rather than a meaningless name like: db_dhruniversity.trigger1.
I always use [a/b]+[d/i/u]_tablename_each as the triggername, that way I always know when the triggers fires (before/after) for which event (insert/delete/update) and on which table.
It's also good practise to document that the trigger fires on each row, hence the each on the end of the trigger name.
Note that MySQL does not support triggers that fire once per statement yet (But that might change in future).