I'm far away from being an expert, but I think the Heegaard Floer homology was invented by Peter Ozsváth and Zoltán Szabó, so I would recommend the following link to you: <a href="http://www.math.princeton.edu/~szabo/clay.pdf">click me</a>

If this Introduction is not enough, you should perhaps read "the original work" (in fact the Heegard Floer homology was developed in a long series of papers): P. S. Ozsváth and Z. Szabó. Holomorphic disks and topological invariants for
closed three-manifolds. To appear in Annals of Math., math.SG/0101206.