Fire is terribly inefficient and expensive lighting (you pay several hundred times as much money per unit of light), is unhealthy (burning a kerosene lamp indoors for four hours a day is like smoking two packs of cigarettes a day), and is bad for the environment (it produces over 200 million tons of CO2 per year worldwide, as well as using 17% of the world's oil.) For details, see this paper by Evan Mills of Lawrence Berkeley National Labs. Fire is also, of course, a safety hazard.
High-efficiency LED's and solar panels provide an alternative that gives higher-quality light, reduces health and safety risks, and could save the poorest people in the world 10-25% of their income every year. The Light Up The World foundation distributes lights like these, and Cosmos Ignite was founded to sell them as a for-profit company.
The Snake Light would provide those benefits, as well as improved usability for the target customers. Its posable neck allows it to be angled down for task lighting without glare, and also allows it to be hung from ceilings, walls, or other objects. It can also be worn around the neck or around the hand like a flashlight; it can even be wrapped around bicycle handlebars or an animal's bridle for travel at night.
Its solar charger could be built in, or could be separate to charge multiple lamps. (Both versions shown above.) At little extra cost, it could also have the lens which focuses the light pull partway out like this lamp, to let the LED shine unfocused and provide broad-area lantern light.
It would be usable for:
A light without the solar panel could be made for as little as $8-10; with the panel, perhaps $20. Even the higher price, while a large sum for the target users, will save people money over time--it should pay for itself in a year, possibly half a year. The cost increase due to the flexible neck should be minimal, while the usability of the light will be enormously improved. Microfinance or payment plans could make them available to those with the least money. Besides saving the users money in the long run, the light will also save their health and the environment, while providing them with better lighting and a more usable form factor than they had before.