ד) הַנְּפִלִים הָיוּ בָאָרֶץ בַּיָּמִים הָהֵם וְגַם אַחֲרֵי כֵן אֲשֶׁר יָבֹאוּ בְּנֵי הָאֱלֹהִים אֶל בְּנוֹת הָאָדָם וְיָלְדוּ לָהֶם הֵמָּה הַגִּבֹּרִים אֲשֶׁר מֵעוֹלָם אַנְשֵׁי הַשֵּׁם:
Rashi, Ibn Ezra, Radak, Ramban (quoting Rashi and Radak), Chizkuni, and Malbim (on Genesis 8:21) all say that they were giants (ענקים). This interpretation is probably based on the only other place where the Nephilim are mentioned, Numbers 13:33, which states
וְשָׁם רָאִינוּ אֶת הַנְּפִילִים בְּנֵי עֲנָק מִן הַנְּפִלִים וַנְּהִי בְעֵינֵינוּ כַּחֲגָבִים וְכֵן הָיִינוּ בְּעֵינֵיהֶם:
Why were they called that? Ibn Ezra and Radak explain that
"ופירוש נפילים שיפול לב הרואה אותם, שיתמה מגובה קומתם."
Ramban and Abarbanel explain that they were the children of the בני האלוהים and בנות האדם.
Ibn Ezra (in his alternate commentary) explains that they were the "opposite of the גבורים" mentioned in that verse. (I'm not sure what that means.)
The פנים יפות (R. Pinchas son of R. Zvi Hirsh haLevi Horowitz, 1700's) says that they were "fallen angels." The תורה תמימה (R. Baruch Epstein, 1900's) says similarly, that they are "those that fell from heaven to earth."
(Please note that "fallen angels," while making first appearance in the Book of Enoch, an ancient Jewish book written in the 1st century BCE, were greatly popularized in Milton's Paradise Lost, published in 1667. As such, it's plausible that these last two commentaries were influenced by Paradise Lost.)