How do CPUs execute instructions in parallel ?

This blog post follows the previous one on the Central Processing Unit (CPU).

“CPU, cores, tasks, hyperthreading, multithreading, user threads, multi-cores”
A lot of vocabulary exists when it comes to parallelism in CPUs / OS.
Moreover, we don’t know exactly what is responsible for what:
Hardware ? CPU ? Assembly ? OS kernel code ? User code ?
I tried to get a better understanding…