Carrier generation and recombination are like a game of hide-and-seek between electrons and their holes.
Imagine you are playing with a bunch of marbles (electrons) and a bunch of holes (empty spaces where electrons could go) on a big piece of cardboard. To start the game, you scatter the marbles around the cardboard and leave some holes empty.
The marbles will start rolling around until they randomly fall into a hole. When this happens, we say that a "carrier" (an electron) has been generated.
But the game doesn't stop there. Sometimes a marble will come out of its hole and leave it empty. When this happens, we say that a carrier has "recombined".
So, carrier generation is when an electron is created, and carrier recombination is when an electron disappears.
This game happens all the time inside a material, like a semiconductor. The marbles are actually electrons and the holes are empty spaces in the atomic structure of the material.
When light hits the material, it can give energy to the electrons and create more carriers. These carriers can then move around and do useful things, like creating electricity in a solar panel or light in an LED. But if the carriers recombine too quickly, all that energy is wasted.
That's why engineers try to minimize carrier recombination to improve the performance of electronic devices. They also try to optimize carrier generation to get the most out of the light that hits the material.