La vista is ‘the view’ and gorda means ‘fat’ (or ‘enormous’ in a colloquial sense). So hacer la vista gorda means to deliberately not see the illegal or immoral things that are happening, you’re simply looking at the clouds and enjoying the view!
Muchas celebridades defraudan a Hacienda y no pagan los impuestos que les corresponden, pero el Estado hace la vista gorda.