Tafsir translates literally into "explaining"; it represents commentary on the meanings of the Qur'an. Ibn Kathir is perhaps the most venerable of the Tafsir commentators, and these volumes are useful for explaining the context of Qur'anic verse, especially when jihad deniers accuse you of taking verse out of context.
Ibn Kathir went into great detail citing hadith and the verdicts of other Islamic authorities to explain the meaning of each of the Qur'an's six thousand-plus verses. His tafsir is widely considered the most authoritative of all Muslim commentaries.