Clear all the stages in a chapter with a gold trophy on each stage (consecutively) to get a gold trophy for the chapter. Now, if you replay the chapter, you can press start and skip any of the stages in the chapter, including the boss. This is particularly useful when going for all the endings, especially for the last chapter. Stage skip for a chapter can only be unlocked by getting the gold trophy on Normal difficulty or above.
To get a gold trophy on a stage, you generally need to get all the gold coins and have a full step combo from the start of the stage to the end. Step combos don't continue if you die and restart at a checkpoint, so if you are going for a gold trophy and you die, then you need to restart at the beginning of the stage.