What does "dynarec" mean?
"Dynarec" is short for dynamic recompiler, ie. a module of an emulator that emulates the CPU by dynamic recompilation.
What is "dynamic recompilation"?
Dynamic recompilation is an alternative term for dynamic binary translation. Instead of "interpreting" foreign binary machine code this technique translates code blocks during runtime ("on the fly" or "just in time") and caches them in the memory to call the translated code when program flow enters that block again.
It's similar to a JIT-compiler for Java, with the difference that we aren't dealing with verified bytecode but with real machine code.