I was very surprised to read on Wikipedia that it is undecidable in ZFC whether "$X\prec Y$ implies $\wp X\prec \wp Y$", see this link wiki. I tried to find out more but could not find any papers on this result. I would have thought this statement is as fundamental as CH or GCH and so should be well discussed.
Can anyone cast some light on this, if this statement were taken as an axiom what would be the consequences, is it related to GCH, and is there a good paper or article on it.
Yes, this is a well-known undecidable statement. It is implied by GCH (which says that $2^\kappa=\kappa^+$, so if $\kappa<\lambda$ then $2^\kappa<2^\lambda$ since $\kappa^+<\lambda^+$). See Easton's Theorem, which - among other things - implies that it is consistent with ZFC that $2^{\aleph_0}=2^{\aleph_1}=\aleph_2$, as well as many similar variations. (Actually, this result holds in Cohen's original model of ZFC+$\neg$CH, although I don't know if this was known prior to Easton's result. EDIT: See Andreas' comment below.)
One reason you won't see much written about this statement is that - unlike CH or GCH - it doesn't seem to have a lot of useful consequences. It's just not very strong - in particular, note that it does not imply GCH. Indeed, we can have GCH fail everywhere and have this statement still hold; see https://mathoverflow.net/questions/138308/woodins-unpublished-proof-of-the-global-failure-of-gch, which describes a result that (assuming large cardinals) it is consistent that $2^\kappa=\kappa^{++}$ for every $\kappa$.
Perhaps surprisingly, the negation of this statement follows from a useful set-theoretic principle, namely the Proper Forcing Axiom which implies $2^{\aleph_0}=2^{\aleph_1}=\aleph_2$. The Proper Forcing Axiom, among other things, implies that there is a collection of five linear orders of size $\aleph_1$ such that any linear order of size $\aleph_1$ contains a suborder isomorphic to one of these five; that any two $\aleph_1$-dense subsets of $\mathbb{R}$ are isomorphic; and a number of other nice things.