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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?

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“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.

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In this case, the "circuits" are more of an abstraction as an encryption scheme, and not specific physical circuits. They are specifying a logic map, such as for Yao's Garbled Circuits.

An approachable introduction is here: http://web.mit.edu/sonka89/www/papers/2017ygc.pdf

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