It has a very literal meaning. Something breaks into pieces, or falls into pieces - deliberately or accidentally. It might be useful to have some more context.

A literal meaning for "come apart" would be to 'separate into pieces'. Looking at the sentence, but without seeing the context it's in, it seems to me like it's probably meaning something more along the lines of 'to go wrong'. Like the phrase "come apart" is to mean the plans being broken. I'm not sure I've seen "come apart" used that way before, but I've definitely seen "fall apart" used in that way many time.