What does it mean by "Adding Gaussian Noise to a 2D Image"?
You can find Gaussian noise generators in many image processing softwares.At each pixel, you add a realization from such random noise generators. You can look for more details at How to Generate White Gaussian Noise. 

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Why Gaussian noise is usually used?
Why is Gaussian noise called so?
What's gaussian noise look like?
The model of noise in Image denoising problem