Those who are in positions of power in any organisation always have more responsibility the higher up they are. In the U.S. Army (or in any army) it's the officers who have the responsibility and the authority to make sure that operations run smoothly. The duties and responsibilities change from one officer to another, but there are a number of responsibilities that every officer shares.
One of the primary responsibilities of an Army officer is to be a leader. Officers are taught (either through academy experience or through experience on the front lines) how to take charge of situations and how to provide a good example. Leadership means that you can coordinate the actions of the people below you while at the same time earning their respect and making sure that you're accomplishing your goals while treating all soldiers fairly. Leadership is a delicate juggling act that often takes both training and experience in order to learn well.
It is also the responsibility of an Army officer to instruct soldiers beneath him in a way that makes them better. If an officer sees there is a problem with a soldier's martial skill, attitude or knowledge, it is the responsibility of that officer to see that it gets taken care of. In some instances that officer may teach the soldier himself, but in most circumstances that soldier is simply remanded to a training course where another officer who specialises in the area that needs improving will ensure the soldier's proper education.
Another responsibility of an Army officer (and one that is a fairly flexible idea) is to fulfil their duty. This particular responsibility can mean many things. Duty was summed up by Gen. John Wickham as "acting in absence of orders based on an inner sense of what is morally and professionally right." Often times an Army officer must make decisions without any input from higher ups, and he must both make those decisions and take responsibility for the results of those decisions.