Helpmate problems ... I don't get "why"

To enhance my tactics training, I created a list of ~35 checkmate patterns (Blackburn's mate, Lolli's mate, etc.) and I am working through them by writing out my own narrative on how to play the pattern.

Today, I picked helpmate from my list and in looking at several sites for definitions/examples, I just don't understand how these problems are used for study. Based on what I've read, both black and white must cooperate to achieve check in x moves.

Why would either side make the best move for "the other side" to mate?

Do these problems represent blunders that would occur in a real game?

No, it's a different discipline totally, selfmates same thing. Even many mate in x# of moves are very often unrealistic. This does not mean that these puzzles are not clever, artistic or beautiful.

It's not chess, it's puzzle-form using the rules of chess.

Rooperi gave you the answer (selfmate puzzles have next to nothing to do with competitive chess) I just wanted to add: 

Your approach in general -- doing the work yourself and making notes about it -- sounds great to me and I think diligently this mindset will engender good results. 

Two great books -- for classic patterns in textbook form the book to get is "how to beat your dad at chess" -- it's all about these mating patterns. Once you've got that down you can test yourself with judit polgars enormous CHESS, which is 90% mates, mate in one, two and three... zillions of em... it's would be great way to challenge and reinforce what you are doing. 

After that (simple) endgame studies are very good for working calculation and tactics. 

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Thanks for the help guys ... I appreciate it!

How to beat ur dad at chess....I bought this for my 12 yr old son, but used it myself...it's great! :0)