Is this language NP Hard?
Indeed, this is the prototypical NP-complete language.

Recall what NP-hardness means: For all languages $L'$ in NP, there is a polynomial time reduction from $L'$ to $L$. 
Normally, when one wants to prove NP-hardness, one takes a language $L''$ which is itself already known to be NP-hard and establishes a reduction from $L''$ to $L$.

But not so in this case! It is much more natural to directly construct a reduction from $L'$ to our $L$, only using the fact that $L'$ belongs to NP.