But Nadab and Abihu died before their father. — Leviticus 10:1-2 tells why: viz., because they offered “strange fire” before the Lord. (See also Numbers 3:4, from which our text appears to be derived.)
And had no children. — Literally, And sons had not become (been born) to them.
Therefore Eleazar and Ithamar. — And Eleazar and Ithamar acted as priests; Numbers adds, “before the face of Aaron their father.” It is implied that the office of the priesthood remained with the two lines, or houses, of Eleazar and Ithamar.