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I am new to Heegard Floer. So far I understand that different HF groups are invariants of a three manifold. But I do not understand what these groups actually measure. I mean it seems to
me that they are not much natural. Can someone shed some light? I need to know what these groups actually measure and also why they are powerful for the study of three manifolds.

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 Have you first tried the numerous expository notes on this subject? Or if you're asking about its use, then a previous MO question? In particular, the latter question is a duplicate-of-sorts: mathoverflow.net/questions/88692/… . I vote to close. – Chris Gerig Sep 18 at 3:17
I second Chris's suggestion to do some more reading before asking a more focussed question. – Mark Grant Sep 20 at 12:13

closed as not a real question by Chris Gerig, Ryan Budney, Tim Perutz, unknown (google), Mark Grant Sep 20 at 12:12

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I know that it can be applied to solve some problems in knot theory and three manifolds. but it does not seem natural to me. It seems like it is equivalent to S-W Floer theory but then many people I know who do Heegard Floer do not have any background in that, what I'm saying is that you lose insight to the problems this way. unless you have the big picture in mind. I think some people who do Heegard Floer are just following what is fashionable.

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This is a contentious, debatable comment that doesn't answer the question asked by OP. – Somnath Basu Sep 20 at 4:11

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