To be stunned or dumbfounded—so surprised or astonished that one's eyes go blank (like dots in cartoons).
彼が突然辞めると言い出して、みんな目が点になった。
When he suddenly said he was quitting, everyone was stunned.
そんな冗談を本気だと思っていたとは、聞いて私も目が点になった。
Hearing that someone took such a joke seriously left me speechless.
彼女の発言に目が点になり、しばらく言葉が出なかった。
Her remark left me dumbfounded and I couldn't speak for a while.