If something happens afterward, it occurs after some original event or time. When kids get out of school at 2:00 p.m., teachers generally go home some time afterward.
You might attend a reading by an author and then go to the reception afterward, or eat dinner with your family and then go out for ice cream afterward. You can also use the word afterwards — although afterward came first, from the Old English æftanweard, combining æftan, "after," and the direction suffix -weard. The original English form, aftward, was a nautical term.