Living hand to mouth means being in a material situation where every commodity (be it money, food, or something else) is needed the moment it's acquired. If you're living hand to mouth, there is no "saving for a rainy day." If a rainy day comes along, you're fucked.
A practical example would be a mom supporting a family working under the table as a housekeeper. She's working under the table because she gets to keep 100% of what she makes, which is barely enough to keep her family afloat, government cheese notwithstanding. She falls cleaning a marble bathroom and breaks her arm. She loses her clients and her income.
"Hand to mouth" attempts to explain why so many people in poverty stay in poverty. When you can't catch your breath, it's hard to catch up.