Memory editors such as Cheat Engine are able to read the memory of other processes and modify it.
How do they do it?(a code snippet would be interesting!) A process does typically not have the ability to access the memory of another one, the only cases that I've heard of are in sub-processes/threading, but memory editors are typically not related to the target process in any way.
Why do they work? In what scenario is this ability useful aside from using it to hack other processes, why wouldn't the operating system simply disallow unrelated processes from reading the memory of each other?
On Windows, the function typically used to alter the memory of another process is called WriteProcessMemory:
https://learn.microsoft.com/en-in/windows/win32/api/memoryapi/nf-memoryapi-writeprocessmemory
If you search the Cheat Engine source code for WriteProcessMemory you can find it both in their Pascal code and the C kernel code. It needs PROCESS_VM_WRITE and PROCESS_VM_OPERATION access to the process which basically means you need to run Cheat Engine as admin.
WriteProcessMemory is used any time you want to alter the runtime behavior of another process. There are legitimate uses, such as with Cheat Engine or ModOrganizer, and of course lots of illegitimate ones. It's worth mentioning that anti-virus software is typically trained to look for this API call (among others) so unless your application has been whitelisted it might get flagged because of it.