Imagine you took the pieces of a 50-piece puzzle and stuffed them in your pockets. Then you went around town, doing your daily activities, dropping a piece here and a piece there. You might leave one at your desk at work and one in the copy room. One will be left on the counter at the post office and another in your grocery shopping cart. One piece will get tucked into your child's backpack and one will be on the treadmill at the gym. When all the pieces are gone, they are so widely scattered that no one will ever be able to put the puzzle together again.
Now imagine that the pieces are figurative and invisible. The pieces to the puzzle are words that you say to your best friend, to your mother, as a comment on a stranger's blog. There may be a story there, but if they are still scattered, no one will ever be able to decipher what was being said.
Or perhaps your words are all delivered to one individual over the course of weeks, months, even years. Maybe they are hints to a special someone how much they mean to you but taken in small doses over time, they don't realize what it is you're saying. Maybe you have given them all of the pieces but they never knew there was anything to be assembled or other meanings hidden within.
Leaving pieces of a puzzle behind is one way to write a mystery (something I have never done) but it can also be used in any type of fiction writing. The pieces may all be leading somewhere or to some revelation that only the author knows. Keen readers might pick up on it before the truth is revealed, while others will only look back and discover that the pieces of the puzzle were there all along, they just hadn't been paying close enough attention.