"Running after" means to chase or pursue something or someone. For example, if a child sees a ball rolling away, they might start running after it to catch it before it goes too far. This action shows excitement and determination to reach what they want. In a different context, "running after" can also refer to trying to achieve a goal or dream. For instance, someone might be running after their dream job by applying to many positions and attending interviews. This pursuit requires effort and persistence, as they work hard to make their aspirations a reality.