That $100 billion/year figure is supposed to be in place by 2020. There’s still several other countries planning to contribute, and others who plan to increase their contributions. Still, wealthier countries can do more. They just print the money anyways. Might as well use if for a good cause.
Poorer countries will start receiving money sometime in the middle or end of next year.
What exactly will the Green Climate Fund do? It will help emerging economies (poorer ones) cut back on greenhouse gas emissions and tackle challenges such as heatwaves, mudslides, etc. Basically, anything tied to the climate.