Fund Rebels is a mechanic which allows you to provide funding to a separatist rebel group in a country for a year. Funding rebels is usually very expensive, depending on the economy, size, etc. of the country, typically it is not worth it to fund rebels due to the immense cost and low chance of impacting a nation, especially if the nation has a good amount of stability. Although, if the country is weakened, and could be near to collapse, this could be able to affect them heavily with the rebels, as it goes with a good amount of time for it.
The separatist rebels enhance the chance of countries breaking away from the victim/funded country, allowing for cooperation with military capital rushes/mass city conquest to collapse countries quickly, This pairs well with the 
United States on defensive and even offensive wars, however can cost a lot, and your military has to be on the spot and ready to quickly attack to pair in conjunction with the rebel funding. This can also enhance the chance of widespread insurgency and if they have it, makes the events from it happen WAY more often. So for your info, basically a way to quickly collapse 
China.
Funding rebels will only work if the nation in question is already having separatists problems. For example, funding rebels in a stable 
United Kingdom will do nothing, but if you are funding rebels in a not-so-stable United Kingdom that's having separatists, the separatist rebels enhance the chance of countries declaring independence from the victim/funded nation.
Funding rebels counts as a diplomatic action, like a war justification. You may also cancel it at any point.
The Fund Rebels screen