Ghiggini has shown that the only knot giving rise to the Poincare homology sphere by Dehn filling is the trefoil knot, as an application of Heegaard Floer homology.
Another important point is that now it is known that certain types of Heegaard Floer homology are computable, starting with Sarkar-Wang. Since it is known to be equivalent to other Floer homologies (Seiberg-Witten, Embedded Contact Homology), this allows one to compute these other invariants. The hope is to be able to get combinatorial formulae for invariants of 4-manifolds from this, which are related to Seiberg-Witten invariants. Unfortunately, sometimes the combinatorial formulae are more intricate and less well-motivated than the geometric definitions, or have the geometry suppressed.
As you noted, many talks on Heegaard Floer homology are getting quite technical, especially the bordered Floer theory. I believe that people think the added complexity is worth the investment, since it should yield new insights (and already is). But this also means that the motivation for some technical results might not be currently apparent.
