Relation between two definition of second cohomology groups.

Question

I have studied in The Schur Multiplier by G. Karpilovsky, that the $n^{th}$ cohomology groups as quotient groups of $n$-cocycles and $n$-coboundries. But when they are defining the second cohomology group, they are using the concept of a central extension. I can not see an explicit relation between these two. Please helps me.