TDY stands for Temporary Duty and thus for military men and women who are deployed on a mission. A widow is someone whose husband passed away. Combined, it is used to express that your partner (husband/bf) is away from home and at times, you feel lonely due to that.
My man is gone TDY again, I feel like he's hardly ever home. I'm a TDY widow
by mimimietje December 03, 2010