It's often used to describe someone who is low in spirits and may be showing signs of sadness such as a drooping mouth or a lack of energy.
For example:
* "He's been down in the mouth ever since he lost his job."
* "Don't worry, you'll feel better soon. Just try to keep your chin up."
The idiom is thought to have originated from the physical appearance of someone who is feeling down. Their mouth might appear droopy or their lips might be pressed together in a sad expression.