What Does the Total Variation Norm Mean in the Context of Image Processing
The Total Variation of an image $ I $ can be calculated in one of 3 methods (See The Meaning of the Terms Isotropic and Anisotropic in the Total Variation Framework):

Anisotropic TV - $ \operatorname{TV} \left( I \right) = \sum_{x} \| \nabla I (x) \|_1 $.
Isotropic TV - $ \operatorname{TV} \left( I \right) = \sum_{x} \| \nabla I (x) \|_2 $.
Isotropic Squared TV - $ \operatorname{TV} \left( I \right) = \sum_{x} \| \nabla I (x) \|_2^2 $.

In practice, all yield almost the same result.
The Total Variation is a measure of how close the image is to a Piece Wise Constant function. Namely, How sparse are the changes in the gradient of the image.
You may read more at Total Variation Denoising.