An assistant director can be called as a manager on a film set. They are responsible to look after the entire shooting process and make sure everything is working as per plan and as per the given schedule.
Their job may not include being creatively involved in the direction process as everyone assumes to be, but to see that everything is working fine and everyone's keeping up wuth their respective jobs well enough.
Assistant Directors, generally referred to as ADs are many in number, working under the main director and based on their performances are ranked as 1st AD, 2nd AD and so on. Some 1st ADs also get to direct some portions of the films if they are trusted by the Director and have skills to do so. Portions like montages, song sequences, crowd scenes, etc, where they have liberty to make a few mistakes and still get away with it are directed by the 1st ADs.