Kidushin 78a #1: All her (primary) seed (i.e. her father's) must be from Yisrael (and not a convert).

Kidushin 78a #2: One of her parents must be a Yisrael.

Kidushin 78a #3: She must be seeded in Yisrael (both her parents are Yisre'elim).

Kidushin 78a #4: She must be a Yisre'elis when her Besulim (tokens of virginity) finish growing (at the age of three, but not if she converted afterwards).

Rashi: This refers to a Kohen Gadol, but some Kohanim may marry a widow, e.g. a Kohen Hedyot.

Malbim: This is another way in which a Kohen Hedyot will resemble a Kohen Gadol. He will marry a Bas Yisrael only if she is a virgin. However, refer to 44:22:2:5.

Kidushin 78b #1: It means, from the Kohanim (i.e. Hedyotim, but not a Kohen Gadol), they may marry a widow. Radak ? Targum Yonasan is like this ? other Kohanim may marry a widow.

Kidushin 78b #2: Kohanim may marry widows of men whose daughters are permitted to Kohanim. This is like the opinion that a male convert's daughter is like a Chalal's daughter. A Kohen may marry Reuven's widow only if he may marry Reuven's daughter.

Rashi: A Kohen may marry an absolute widow, but not a divorcee or Chalutzah ¹ (she fell to Yibum, and did Chalitzah). The latter, even though they are single, are forbidden even to a Kohen Hedyot.

Radak: This will be an added Kedushah. Even a Kohen Hedyot will be permitted to marry a widow only if she was widowed from a Kohen Gadol or Kohen Hedyot.

Malbim: If a widow is a Bas Kohen, and her first husband was a Kohen, a Kohen Hedyot may marry her; he will not be totally like a Kohen Gadol.