Let me show you a classic and often imitated Sicilian Dragon game:
A great game you would most likely agree, no? In fact, this game was basically a world championship game (because Fischer did not defend his title in 1975). So this game was very important to the history of chess and to the theory of the Sicilian Dragon; but did going over the game make you markedly better?
A great way to improve at chess is to ask questions and to get the answers to those questions from a stronger player, mentor, teacher, strong chess program, etc. Let me give you an example of what I'm talking about.
Notice the lower ratings of these players. The best games to go over are: 1. your own games 2. games of players rated similarily to you
These players are making mistakes that you are making (the GMs are not). "Don't learn from your mistakes, learn from the mistakes of others". The quote is being a tad facetious. You can gain a lot by learning from the mistakes of yourself but also (and this is what the quote is trying to portray) can save yourself hassle and lost rating points by learning from the mistake of others.
Puzzles we should have learned from the above game: