There are different levels of objectives that each side had in this war.

On the highest level, the objective of the Confederate States was to become independent.  They wanted to break away from the US and be recognized as a separate country.  The objective of the United States was to prevent this from happening.

Of course, each side had lower-level objectives that they needed to achieve in order to accomplish their overall goals.  For the South, the main objective was to keep from losing.  If the South could manage to remain “alive” long enough, the North might decide that the war was not worth it and give up.  For the North, the goal was to take control of the South.  The North needed to actually invade the South and control its territory.  It also needed to prevent the South from getting weapons and other support from Europe so that the South would not be able to hold out as long.

The South had the easier objective to achieve in this war.  It only had to hold out long enough to make the North give up.  By contrast, the North had to invade and control the South.  This was a much harder objective.