Meaning of Multiplying a complex number with its conjugate
Multiplying a complex number with it's conjugate yields the squared magnitude of that complex number. 

However, in your formula, you are multplying the signal with the conjugate of the N samples delayed signal, take the squared magnitude of that (thus dropping phase differences between the signal and delayed signal, which would result from a frequency offset) and average it over Ng sample times. This means you are calculating the autocorrelation of the signal at a time delay of N sample times.

I assume the formula is from an algorithm for coarse symbol timing estimation for OFDM signals. The pseudo-random pilot sequence of length N is repeated twice. It's autocorrelation thus has a peak at N. Now, if you want to estimate the timing offset, you just take the time index of this peak.