Why in thermodynamics, some reactions are taken at constant temperature and pressure? What is its significance? To be more specific while deriving relation between cell emf and free energy, constant temperature and pressure  assumptions were taken. Why?
If you read my answer to this question: Why does the Gibbs free energy only correspond to non-expansion work?, you will see that

$$\mathrm{d}G = V\,\mathrm{d}p - S\,\mathrm{d}T + đW_\text{add}$$

Of these three terms, only $đW_\text{add}$ is related to the electrochemical work. Therefore, in order to equate $\mathrm{d}G$ to $đW_\text{add}$, you have to assume constant $p$ and $T$ such that both $\mathrm{d}p$ and $\mathrm{d}T$ are equal to 0.

In general, this applies to chemical equilibria as well. Because of the above expression, we can say that $G$ is the "natural quantity" to use in systems with fixed pressure and temperature. If instead you had a system with fixed volume and temperature, the Helmholtz free energy would become much more relevant.