I have gotten more than a few questions on the reasons behind aeration of the greens and, to a lesser extent, the tees and fairways. The following video does a great job of explaining the reasons.
The main takeaways from this video are:
1) Relieve compaction.
2) Reduce organic matter build-up.
3) Provide passageways for water and oxygen to move through the soil.
The sand top dressing also has the added benefit of smoothing the putting surface.