Correct spelling, explanation: nationalities is a noun whose singular form is nationality. The origin of the word can be found in the word natio, which was a Latin expression for people or nation, and from a French form nationalite. In fact, nationalities comes from the adjective national.

Definition of nationalities:
1. noun (plural) – when you belong to a particular nation,
The competition is open to all nationalities so do not hesitate to take part in it.

Phrases with nationalities:
A few commonly used phrases with nationalities are: represent nationalities, hold two nationalities, and minority nationalities.
Fifty flags which you can see on your left represent all the nationalities that belong to the union.
His mother is British and his father is American so no wonder that he holds two nationalities.
This part of the town is popular among minor nationalities and maybe because of that is rather poor.

Incorrect spelling, explanation: the rule says that when a noun ends with a -y letter that appears after a consonant, we have to change this -y letter into -i and then add an -es ending while forming a plural form of this noun. That’s why the plural form of nationality is nationalities. Many English users, however, tend to forget about this rule and they spell nationalities as nationalites, which is wrong.