I think, (though this is only may experience, so I don't really know) that once one has sufficient understanding of the shapes involved that the moves begin to make natural sense, especially once you see them, and so understanding the general reason behind each move, or noting that a particular move was a mistake, enables you to remember the move itself in context of the whole board position. Which is why I think this ability usually increases the stronger you get.

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"Those who calculate greatly will win; those who calculate only a little will lose, but what of those who don't make any calculations at all!? This is why everything must be calculated, in order to foresee victory and defeat."-The Art of War