Poking the skin with pigments to create an image won't stop the crop of hair that grows across that bodily surface. Say you decide to decorate your forearm with an animal symbol that represents "strength." You visit a reputable tattooist who creates a picture of a tiger, complete with regal black stripes on a tawny coat. Your tattoo professional shaves the area that will serve as the landscape for your vibrant statement. As the artist works, inks are injected beneath the thin outer epidermal layer of skin and into the meatier dermis, which also houses blood vessels, glands that make oil or sweat, specialized nerve cells, and a forest of hair follicles.
As your fresh tattoo heals, your dermal neighborhood goes about business as usual. Following its regular growth cycle, hair continues to spring up through the dermis and epidermis. Now consider the look of your nice new artwork. If you are particularly hairy, that bold black-and-tan emblem might start to take on a different, slightly less powerful, appearance (and require routine shaving to bring back the tiger's smooth coat).
As they say, you may want to think before you ink. Or, at least, watch out for whiskers when you pick the terrain for your tattoo!