My understanding is largely ten years old and high level and only for one kind of fully homomorphic encryption. Things have changed and there is more than one kind.
I heard it described as a system that encrypts each bit and then evaluates the "encrypted bit" in a virtual gate-based circuit that implements the desired operations that one wants applied to the plaintext. The key to (de|en)crypt plaintext will be at least one gigabyte. Processing this exponentially larger data is why FHE based on the system I've described is so slow.
So, if you wanted to, say, add numbers, that would involve implementing a full adder [0] circuit in the FHE system.
I heard it described as a system that encrypts each bit and then evaluates the "encrypted bit" in a virtual gate-based circuit that implements the desired operations that one wants applied to the plaintext. The key to (de|en)crypt plaintext will be at least one gigabyte. Processing this exponentially larger data is why FHE based on the system I've described is so slow.
So, if you wanted to, say, add numbers, that would involve implementing a full adder [0] circuit in the FHE system.
[0] https://en.wikipedia.org/wiki/Adder_(electronics)#/media/Fil...
For a better overview that is shorter than the linked 250 page paper, I encourage you to consider Jeremy Kun's 2024 overview [1]
[1] https://www.jeremykun.com/2024/05/04/fhe-overview/