A Jew is traditionally defined as either a person of Jewish descent, or a person whose religion is Judaism. A Gentile is a general term for any people not Jewish, either by descent or religion.
A person can be Jewish by birth or conversion. In the case of birth, Jewish status typically passes through the mother. Orthodox, Reform, and Conservative movements in Judaism all have differing requirements in the case of Jewish descent. Whether a person born of Jewish parents identifies as a Jew is a consideration, while some branches hold to more strict views regarding observance of the Torah.
Someone born a non-Jew can still become one by a process of conversion. Jews do not typically try to convert non-Jews to Judaism, but do provide a means of learning about the religion and observing the customs if a person truly wishes to pursue it.
The word "Gentile" is not a word of Hebrew origin. It was brought into English during the Middle Ages via the Latin word "gentilis." The equivalent word in Yiddish is "goy" (plural "goyim"), and comes from the Hebrew word for "nations." The word "Gentile" has also been adopted by the Mormon Church to refer to non-Mormons.