- You have to push this button.
- You have to just push this button.
What role does the word 'just' play in the sentence above?
You have to [just push this button].
The adverb "just" is a focusing modifier here. It's modifying the verb phrase "push this button". It means that all you have to do is push this button, and do nothing else.
just is suggesting an exact idea of how to do something.
The Oxford English Dictionary has a definition:
Exactly, precisely; verily, actually; closely
Without it, it's simply a blunt command to do something.
With it, it's proposing a specific task that will precisely accomplish what's needed.
Just kill him!