Hardwired secret key in public / private key encryption I am new to cryptography and I need to know some details about the hardwired keys. 

Taking as an example the paper "Multi-Input Functional Encryption", a key is hardwired in the description of the key generation scheme.

Is this technique related to encryption schemes or it is a form of circuit construction?
“Hardwiring” an input into a (say, Boolean) circuit usually means taking a circuit $C$ with two inputs $x\in\{0,1\}^n$, $y\in\{0,1\}^m$ and then fixing the inputs corresponding to $y$. This gives the circuit $C_y$ that for every $x$ returns $C(x,y)$ [AB]. Thus, hardwiring is more about circuits and has nothing to do with encryption schemes.

In the example of multi-input functional encryption, the circuit $\mathsf{G}_f$ can be seen as a function that takes a master secret key and $n$ ciphertexts as input. By hardwiring a particular $\mathsf{MSK}$, you are fixing the first input to the circuit $\mathsf{G}_f$ to this $\mathsf{MSK}$.

[AB]: Arora and Barak. Computational Complexity: A Modern Approach.