'Liver' spots - a.k.a. Age spots, Senile freckles, Senile lentigo & etc. are small brown freckle-like areas of darkened skin which often appear in light-skinned individuals as they age.
They are mistakenly named, and have no connection with liver function (the name probably arose from their brown colour).
Although it's known that they are the result of increased melanin, and are related to sunlight exposure, there is currently no agreed explanation as to why they tend to proliferate with increasing age. In addition the underlying process of their formation is unknown.
See : Wikipedia