godan verb (-mu), expression
hold one's tongue; shut up; keep silent
Idiomatic expression meaning to deliberately refrain from speaking, often to keep a secret or avoid conflict. The verb つぐむ is almost exclusively used in this phrase.
彼は何も言わずに口をつぐんだ。
He held his tongue and said nothing.
その話題になると、みんな口をつぐんでしまった。
When that topic came up, everyone clammed up.