To choke up or be rendered speechless (unable to speak because of surprise, emotion, etc.).
彼女の突然の告白に言葉を呑んでしまった。
I was left speechless by her sudden confession.
式典で名前を呼ばれ、緊張して言葉を呑んだ。
When my name was called at the ceremony I got nervous and was speechless.
感動的な場面を見て、皆が言葉を呑んだ。
Everyone was moved to silence by the touching scene.
To hold one's tongue; to refrain from saying something one wants to say.
上司の前では部下もたいてい言葉を呑むことが多い。
Subordinates usually hold their tongues in front of their boss.
彼は本当は反論したかったが、場の雰囲気を壊したくなくて言葉を呑んだ。
He actually wanted to argue back, but he held his tongue because he didn't want to ruin the atmosphere.
怒りを覚えたが、相手のことを考えて言葉を呑んだ。
I felt angry, but I held my tongue out of consideration for the other person.