As far as I understand, these lines work like this:

1. NN is an integer variable defined somewhere above;
2. idx is expected to be a list of integers not exceding NN so that Complement[Range[NN], idx] returns a non-empty list of indices that are in Range[NN] but not in idx;
3. Matrix A must be NN * NN square matrix;
4. By calling function SC first you take A's rows and columns specified by the idx list and then subtract from it a dot-product of three matrices: a matrix formed by A's rows from idx and A's columns from the complement of idx, the inverse of a matrix formed by A's rows and columns from the idx's complement and finally a matrix formed by A's rows from the idx's complement and A's columns from idx.

The last sentence is rather sophisticated but I hope it clarifies these lines of code a bit. Good luck!