Please see the documentation for Subscript:
http://reference.wolfram.com/language/ref/Subscript.html
Subscript is mostly useful for creating formatted output for reading. I would only suggest using Subscripts in code to experienced Mathematica programmers. Subscripted variables are full expressions and this creates confusion with newer programmers.
With[{xn = Subscript[x, n]},
Subscript[x, n + 1] == 2 f[xn] f'[xn]/(2 xn^2 - f[xn] f''[xn])]