rushing off in a flurry; scurrying unprepared
Describes hurrying somewhere in a fluster, often because one was caught off guard. The literal image is grabbing a sword and dashing out without properly securing it.
Hearing the fire alarm, he rushed to the scene in a flurry.
rushing to an emergency with sword in hand
Literal historical sense: dashing out with one's sword drawn because there was no time to fix it at the waist. Rarely used outside historical or explanatory contexts.
Originally, 押っ取り刀 referred to rushing to an emergency with one's sword in hand, without time to affix it at the waist.