It is well known that Jews who keep kosher wait after eating meat before eating milk (for one, three or six hours, depending on custom), because the meat can leave an aftertaste or get stuck between your teeth. Less well-known is the chumrah, stringency, that many have of waiting up to six hours after eating hard cheese before eating meat for the same reasons (Rama, Yoreh De’ah, 89:2.).
Some define hard cheese as cheese aged for six months or more. (By this definition, Parmesan is probably the only commonly eaten cheese in this category.) Others refer to cheese that is fermented with worms (which used to be quite common) or criteria based on the texture.
According to most authorities, hard cheese that has been melted no longer counts as hard cheese. What the poskim call “American cheese”, something like cheddar that has been melted, had additives mixed in and then resolidified, is also not considered hard cheese. If in doubt, ask your rabbi.