The phrase "Apples and Oranges" is used to colloquially indicate a false analogy, or a false comparison, even though apples and oranges do belong to same class of things--fruits--and would thus seem to have qualities in common. Like any idiomatic phrase, "Apples and Oranges" has accumulated a meaning different than the individual words used within it.
French Canadians use the phrase in French, which is "comparer des pommes avec des oranges." Across Europe, the supposedly mismatched fruits in the idiomatic phrase are generally apples and pears.
Idiomatic phrases are culturally, not linguistically, based. The phrase "Apples and Oranges" does not have the same meaning in British English. In Britain, the comparable idiomatic phrase is "Chalk and Cheese."
Take care when using "Apples and Oranges" around people who are not native to the United States, even those who speak English well. For example, some Europeans who learn English learn British, not American, English.
The phrase "Apples and Oranges" also serves as the title for a Pink Floyd song about mismatched lovers.