I am confused how gaussian processes and kriging are related? Can anyone please give me some simple explanation. I tried to go through the wiki but I didn't get it
If the points in space are measured with normal random errors the measured points in the plane for Gaussian spatial process. When the process is Gaussian the kriging estimates are maximum likelihood as well as minimum variance unbiased.
The phrase "Gaussian process" is often used in two different ways: (a) to refer to a class of stochastic processes and (b) to refer to technique in machine learning.
Kriging is essentially another name for the same technique, but developed in the spatial statistics literature rather than the kernel method machine learning literature. So if you're referring to the method of Gaussian processes, I think you can safely say they are the same thing. the use of the term usually reflects one's background.
Of course the technique assumes that the data arise from the stochastic process that bears that name. Gaussian processes are just any stochastic process for which any finite linear combination of samples has a joint Gaussian distribution, and also come up in many contexts that have nothing to do with either spatial statistics or machine learning.
Rasmussen and Williams give a great discussion of the machine learning method of Gaussian processes and its relation to other methods, such as support vector machines and neural networks, in their freely available book.