The phrase "mild cheddar" refers to a type of cheese that has a gentle or mild taste. It is not very strong or spicy, but instead has a smooth and subtle flavor. Full definition
We used a mix of sharp cheddar & mild cheddar cheeses. (epicurious.com)
I only had mild cheddar on hand, would have been much better with sharp. (epicurious.com)
I like using mild cheddar cheese so that it doesn't overpower the rest of the soup, but you can certainly use sharp if you prefer. (browneyedbaker.com)