probability - Intuitive explanations for Gaussian distribution function and mahalanobis distance

I was wondering If anyone could give intuitive explanations for the multivariate Gaussian distribution function and mahalanobis distance? My professor didn't explain these in probability class, they were only defined...

Where did the formula come from? Why is the Gaussian function the way it is? Is there a way to intuitively explain mahalanobis distance?

Thank you for any support!!

Answer

For the Mahalanobis distance, have a look here and here