to gird: to fasten something tightly around the waist with a belt or band
At its core this is a plain, physical verb. You wrap a belt, sash, or cord around your waist and cinch it tight, whether to hold up a garment, to hang a sword at your side, or to tie on a rough piece of sackcloth. Everything else the word does grows out of that one simple action.
Because loose robes were the everyday dress, the waist was where you got ready for anything. So girding became a picture of readiness: you tucked and belted your clothing before you ran, fought, traveled, or worked. The same act could equip a soldier (a sword bound on the thigh), dress a priest (the sash that completed his vestments), or signal that a person was set to move.
The word also carries strong emotional weight. To gird oneself with sackcloth was the standard gesture of grief and mourning, a way of wearing sorrow on the body. And poets stretch the picture further: hills can be girded with joy, a strong woman girds her waist with strength, and God can be pictured belting on power. In every case the literal action of belting the waist stays in view, which is why a single word can run from a soldier's sword to a mourner's sackcloth to a metaphor for being clothed in strength.