Aspects
Aspects form when two planets are a certain number of degrees apart from each other. Depending on their distance apart, aspects signify certain things about the relationship between the two planets and indicate whether they will generally have beneficial or challenging effects.
Oppositions
Oppositions form when two planets are about 180 degrees apart from each other (depending on the orb used). The two planets are literally on opposite sides of the chart in this formation.
Oppositions are generally challenging in their nature. Each planet involved wants to exert its influence on the chart at the expense of the planet it is opposing. This can create some difficult situations as a result. The goal for these aspects is maintaining some kind of balance between the opposing energies, as when one side becomes favored too much, the other usually creates some difficult circumstance to restore the balance again. Though many might consider oppositions to be "bad", in reality they frequently create points of conflict that help a person strive to progress in their lives.
The Aspects