To be interrupted or come to an end; something continuous is broken off, paused, or cut short (e.g., conversation, signal, flow).
電話の電波が悪くて会話が何度も途切れた。
The phone signal was poor and the conversation was cut off several times.
話が急に途切れてしまい、気まずい空気が流れた。
The conversation suddenly halted, and an awkward silence followed.
作業が忙しくて昼食をとる時間が途切れた。
Work was so busy that my lunchtime got interrupted.