What is the logic behind Jacobi iterative method? The book I follow and on net also, all that I can find is the algorithm to find the solution, but I don't quite understand the physical significance or logic behind the algorithm.
Can someone please help.

You are trying to solve $A \textbf{x} = \textbf{b}$.
The matrix $A$ could be written
$A = D + N$ where $D$ is diagonal.
If the sequence $\textbf{x}^k$ generated by $D\textbf{x}^{k+1}  = b - N\textbf{x}^k$ converges, then you have $D\textbf{x}^{\infty}  = b - N\textbf{x}^{\infty}$ or $A \textbf{x}^{\infty} = \textbf{b}^{\infty}$.
If $A$ is diagonal, then $N=0$ and there is no iteration to do.
The condition for convergence is $|| D^{-1} N || < 1$. Intuitively, not super accurate but helpful, think that in the iteration $\textbf{x}^{k+1} = D^{-1} b- D^{-1} N\textbf{x}^{k}$, the error term $D^{-1} N\textbf{x}^{k}$ gets smaller after each iteration and the equation approaches $\textbf{x} \approx D^{-1} b $.  There is a theorem for this, look up if you want rigor.
