Archaeologists can tell you that a person's garbage tells a lot about them. It is often all that's left of a civilization, and they will go to great lengths to put potsherds together to see what they have.
In modern times, our trash can also tip off others. Even the absence of trash can tip off others. For example, a dustbin full of brightly colored paper with "my little pony" can tell us that perhaps there is a little girl in that household. We wouldn't expect the husband's drill set to be wrapped in "my little pony" wrapping paper--unless, of course you were Senator McConnell's wife pulling a practical joke.
Police are now advising households to camouflage trash so thieves cannot be tipped off on what you bought for Christmas. Some suggestions include burying the trash under the house (you know, where you buried the umpteenth possum you killed when it got into your attic), cutting the boxes into little squares and farming it out to the local schools for "art supplies", or just shredding it.