First of all, thank you for asking such a good question. It is one of the best questions I have read on this forum.
My "aha" moment was when I read the first words of Cecil Purdy in Guide to Good Chess. He deepened my love for chess, as his own love for the game was so contageous. His knowledge is profound, his writing beautiful - and I feel truly blessed to have this wonderful book by one of the true "saints" of chess.
stwils
i like videos
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Wasn't so much a book, but rather playing continually for nearly a month at chess.com. Simple things really, but for whatever reason they eluded me previously:
1) Castling is just as important to mobilize the rook as it is to protect the king. Therefore it is strongly advantageous to castle as early as conceivably possible.
2)Nothing beats the Italian on white - forget all the exotic gambits. Just e4, kings knight out, king's bishop out, d4, and then castle - bam, bam, bam, bam.
3)If the opponents king is all bottled up and inaccessible and the opponent's queen is out, then forget the king and go after the queen and try to checkmate her.
I'm not well-read when it comes to chess, but Yasser Seirawan's Winning Chess Tactics is wonderful for the beginner. He explains things in a very clear, entertaining manner. If I were teaching a class on chess, this would be the textbook.
Josh Waitzkin's Academy attached to Chesmaster 10th Edition is awsome. I bought it for 25 zlotych (about 7 bucks) and now I enjoy hours and hours of great lectures 
Honestly, and you probably already know this to an extent, you aren't going to really experience many "AHA!" moments in a chess book. Every time I felt that I had one of those moments I was either in the middle of a game, or more often playing through/watching someone elses game. There are certain lines of certain openings that might make you say AHA! and certainly you could find this in a book. But if you are talking about a full on chess epiphany, you will almost certainly find those exclusively in your own games whilst sporting your smartest thinking cap :)
The Amateur's Mind Turning Chess Misconceptions Into Chess Mastery, gave me alot of aha moments, and my rating* rocketed about 200 points straight away after I read it, and they are still heading upwards. And I'd say it makes me understand a position alot easier.
* My live rating on chess.com
Fonix
I'm not really looking for an epiphany, just something that you read or used that helped you understand some aspect of the game more clearly. Again, not something that necessarily worked for everyone else it just that once you used that book or that software or watched that DVD you said to yourself "Man, I wish I had done this earlier because now I understand this aspect way more clearly." It doesn't mean your going to become a GM because you read it just that you now understand what your looking at when you see it.
I enjoy Chessmaster. (grandmaster edition)
I would say Jerry Silman's Endgame book. Not just because of the information it presents on Endgames, which IS awesome but more importantly it changed how I approached every aspect of chess study!!
The other aha moment was when my coach showed me how to really analyze my games for maximum benefit and I quickly noticed it paying off!
Thank you to those that posted. I will definitely add your suggestions to my library of must purchases.
Modern Chess Tactics & Attack & Defence in Modern Chess Tactics (I know that's 2 books but they are both by the same author - Ludek Pachman). These two books really helped me to develop my middlegame. Mind you I still have vast room for improvement!
Good question. I owe a lot to several books but it was mostly a gradual accumulation of knowledge and experience. I first seriously studied chess back in the 1980s. At that time "Modern Chess Openings: Theory And Practice" by Horowitz and "My 60 Memorable Games" by Fischer were my main sources. I went through both books, especially Fischer's, many times, learning a lot each time. No real "Aha" moments that I remember back then, though. All that time I knew I was missing something important. Then I stopped studying and only occasionaly played for about 15 years.
I recently started studying chess again and found what I had been missing. Strategy. I found it in a couple Silman books and a book by Seirawan. There was kind of a collective "Aha, THIS is what my game has been missing." I think of it like erecting a building. Tactics are the foundation, frame, roof, and all parts of the structure. Strategy is the design. If you know tactics you can build a good strong building but you need strategy to design a masterpiece.
All parts of my game need a lot of work but I put in years of study that laid a good (I hope) foundation. I'm excited that I've found a new (to me) and different way of looking at chess. I'm going to have a lot of fun.
"Aha" moments often (I think) have a 'staw that broke the camel's back' quality... you gather knowledge and experience but stay at a certain plateau and then one day the pieces fit together and you move up to the next level.
Some aha's --
I'm not a big fan of Bruce Pandolfini, but his "Pandolfini's Chess Puzzlers" is a wonderful little book. 111 little endgame puzzles. For some reason (see first paragraph of this post) doing those puzzles opened my eyes to endgame tactics -- i went overnight from dreading endings, to loving them. (This is NOT a book of endgame studies) I suddenly got it: there are lots of tactics in the endgame. Pandolfini's favorite theme in the book is quiet moves that take away all the opponent's good moves leaving him in zugzwang.
Jeremy Silman's "Reassess your chess" & "The Amateur's Mind" there's nothing in Reassess your chess that you can't figure out on your own... (Of course, there's nothing in The Calculuus you can't figure out on your own, either -- if you're Newton or Gauss.) ... but I got several small aha's and a couple big ones from RaYC. So: Doubled pawns aren't necessarily bad. In fact, they have their good side -- they open up files for you to attack from, etc. Now a good player reads that and says "Duh, yeah, and water is wet." But I read it and went, "omg?! This makes sense!"
Mastergames Going over master games carefully led me to an aha appreciation of what initiative was and how much more resourceful and creative and at the same time logical one could be.
Discussing and reviewing games and puzzles with strong players -- a big aha here when I suddenly understood -- wow, these people see the board very clearly and have no fear of calculating multiple lines deeply looking for the exclamation point moves on both sides. They look for all the moves they can, they test their own ideas to try to make them fail and AHA: They think a lot harder than I've been... I've got to think harder if I want to keep up!
Playing a very strong opponent here on chess.com I was looking forward to freeing my game castling queenside when I saw that my opponent make a move which set up an attacking combination not on where my pieces were, but where they were going. AHA! I wanna learn to make moves like that!"
I would like to second KJT's suggestion of Winning Chess Tactics by Yasser Seirawan. I was really struggling with tactics until I read this book. Sure I understood what they were in theory (I could describe a pin/fork etc) but actually seeing them 2 or 3 moves ahead was difficult for me. Something "clicked" (my aha! moment) when reading through this book. I became a much better player (I gained around 200 USCF points over the next 6 months - not that I am very advanced at this point, mind you) after reading that particular book.
I've now read three Jerry Silman books and each one of them has given me an "aha" moment several times over. I think that his literature is fantastically designed for people like us, who want to get better but aren't sure what needs to improve. "The Amateur's Mind" is an excellent read which focuses on the mindset of beginners and why they make the mistakes they do. "Reassess Your Chess" Is excellent for someone a bit more advanced, say 1400-1800. His endgame book is really a good read as well, so I would definitely suggest checking out some of his literature. :)
I have a question that I hope can get some good input. As I read the posts in these forums, I often see people ask for advice on what to study to improve. My question is along the same lines but slightly different. I would really like to know what single book, DVD or software helped you understand one aspect of chess much better. for instance....this aspect of your game was suffering until you read this book or watched this dvd or started using this program. What gave you your Aha! now I get it moment. It would be helpful if you focus on something that worked for you. I'm not looking for the Amazon bestsellers or what everyone else says is good but what worked for you on one single aspect of improvement in your game. It can be any one thing from tactics, to middlegame strategy, endgame, openings. What one chess book, DVD, or software do you wish someone had told you about or you had found a little sooner. I hope to build a good library from everyone's selection. I'll start out by saying that I wish someone had told me about Pandolfini's Ultimate Guide to Chess as my first chess book. Is it an ultimate guide, no. It helped me see the board differently though with regard to protection of pieces for a beginner. I liked the student teacher question and answer format. It has some corny jokes but I would recommend it to all beginners. Thanks to all that offer input.