O(n^2) means Big-Oh, n-squared.
O(n^lg^n) is a typo and should read O(nlgn)
(that is, n times log(n))
Both are rough descriptions of the running time of a program. With n inputs, the running time of an O(n^2) program increases by approximately four times whenever you double the value for n. For O(nLgn) the running time increases much more slowly.