I wonder why in assembly there are often included symbols as a language feature and what's the purpose of it?
I suspect that you are confusing op codes and registers for symbols. What is boils down to is that assembly language is just mnemonics for machine language. There really are no weird symbols, however, it is important to understand the architecture of chip that you are coding for.
To get your head around it, consider an easy architecture like the 8085 (https://www.tutorialspoint.com/microprocessor/microprocessor_8085_instruction_sets.htm). The Architecture is not as complex as the x86 and the assembly instruction was meant to be hand coded.
The language I think of that has weird symbols is APL (https://en.wikipedia.org/wiki/APL_(programming_language)). I will defer to the wikipedia article as there are some wonderful examples.