What is this plane and what are the rockets on the back used for?
As the source linked next to the image in the other question says, it is a C-130 performing a "rocket assisted takeoff".

These are performed to safely achieve V1 on short airfields, where the aircraft would not be able to take off otherwise.

The rockets (or "bottles") use solid fuel, so they are usually single-use.

I have no data on the thrust provided by one of them, but the wikipedia article mentions that a "smaller version" made for the civilian market, could deliver "250 pounds of thrust for 12 seconds", so it is reasonable to expect that the thrust provided by the larger bottles would be larger.