What is Galois Field When I am reading some algorithm related to error correction. To generate some polynomial it uses finite-field which is Galois field. I am not from mathematical background. Can anybody explain me in simple form to understand this ?

Galois field is the name that engineers (and especially those studying error correcting codes) use for what mathematicians call a finite field.  In applications, the most commonly used Galois field is $\text{GF}(256)$, also called $\text{GF}(2^8)$.  Its elements can be thought of as polynomials of degree $7$ or less with binary coefficients ($0$ or $1$).  Addition of two field elements is addition of the two polynomials with coefficients being added modulo $2$.  Multiplication is polynomial multiplication modulo a polynomial $m(x)$ of degree $8$, that is, multiply the two given polynomials (which may result in a polynomial of degree as much as $14$) and then divide by $m(x)$, throwing away the quotient and keeping only the remainder.
