The Shulchan Aruch (Even Ha'ezer 2:8; listen to audio for precise citation) writes, based on the Gemara in Masechet Pesachim, that an Am Ha'aretz an unlearned Jew should not marry the daughter of a Kohen, and if he does, the marriage will not be successful. The reason for this Halacha is that the marriage of an Am Ha'aretz to a girl from Aharon's descendants is a disgrace to Aharon and an infringement on his special stature. And by the same token, the marriage of a pious, scholarly boy to a girl from Aharon's descendants brings honor to Aharon and the priestly tribe.
What exactly does the term "Am Ha'aretz" mean for purposes of this Halacha? What credentials are necessary to allow one to marry a Kohen's daughter?
This matter is subject to debate. Some Poskim maintain that so long as a person recites Shema and wears Tefillin each day, and observes the basic Halachot concerning permissible and forbidden behavior, he is not considered an Am Ha'aretz. According to others, however, beyond basic observance, a person must occupy himself in Torah study each day as well in Gemilut Chasadim (acts of kindness) in order to divest himself of the status of Am Ha'aretz.
The Noda B'Yehuda (Rabbi Yechezkel Landau of Prague, 1713-1793), in one of his responsa, notes that many people superstitiously follow the admonition of Rabbi Yehuda Ha'chasid (Germany, 1150-1217) that one should not marry the son or daughter of someone with his or her name. Lamentably, he writes, these same people, who are so careful regarding this matter, which has no Talmudic source, give no concern to the explicit warning that a Kohen's daughter should not marry an Am Ha'aretz. The Noda B'yehuda writes that the explicit laws of the Gemara should be given no less consideration than the warnings of Rabbi Yehuda Ha'chasid. Moreover, the Gemara describes marrying off one's daughter to an Am Ha'aretz as comparable to "placing her in front of a lion." When choosing a spouse for oneself or for one's child, one must look primarily at the prospective mate's Midot (character traits) and level of Torah observance, rather than superstitious concerns regarding the name or other factors of that nature.
As Chacham Ovadia Yosef writes in Yechaveh Da'at, this is especially important regarding the daughter of a Kohen; one who marries a Kohen's daughter must be particularly careful to remain strictly observant and worthy of marrying a descendant of Aharon Ha'kohen.
