Write down the main points of the talk.

Literal

Talk [possessive-の] main-points [object-を] write-down [soft imperative-なさい].

書き留める ('to write down, jot down') is a compound verb: 書く + 留める ('to stop, fix in place'). 要点 (ようてん, 'main points, essentials') is standard academic vocabulary. Another classroom instruction using ~なさい.