These variables can be thought of as directly mapping into the processor.
The CPU can't easily work on numbers that are only stored in RAM (memory). Instead, there are a couple of "slots" in the die itself, where numbers can be stored and accessed at an enormous speed (much faster than RAM or an HDD). These are called registers and have names like EAX, EDI, ECX, EBP, ESP, ... The E simply stands for extended (32bit), the suffix (AX, DI, BP, ...) is for some kind of use-case (AX is accumulator, SP is stackpointer, you get the idea).
Obviously the daedalus variables EAX, EDI, ... don't actually map to the register, because registers don't have an address. However, the actual register value is transfered into the daedalus variable before the daedalus function is called, and transfered back when execution has finished.
If you don't know x86 assembly (and don't want to learn it), there are a couple of "shortcuts" one can remember:
When a __thiscall function is executed, the this-pointer is stored in ECX (this can change during the function, but will always be true at the beginning).
After a function has been called, the return value (if there is one) will always be in EAX.
Parameters are usually passed via the stack and ESP points to the top of it. Because the stack grows from the top to the bottom (like a bat, hanging from the ceiling), this means that at the beginning of a function, parameters are at ESP+4, ESP+8, ... respectively.