To eke out is to get by with difficulty or a struggle. When you just eke out a living, you live from check to check, barely managing to pay all your bills.
You'll often find eke out followed by "a living," or "an existence," describing the process of working hard for every bit of money. You can also use it to mean "squeeze out," or "win after a struggle," the way an underdog baseball team just barely ekes out a win over its rival. And finally, you can make something last longer, or eke it out: "She'll eke out that chili for a whole week, I bet."