This phrase is not about actual shirts but describes someone willing to give anything to help. Though it's an expression, no one's really expecting you to give away your clothes.
Pro Tip 2/3
Figurative Generosity
Use this phrase to highlight selfless generosity, even if it's not a material object given. Without hesitation, he gave the shirt off his back by donating his last $10 to the charity.
Pro Tip 3/3
Not Literal
Don't misinterpret the phrase; it's not about helping at a cost to one's basic needs. She offered the shirt off her back, but she still made sure her own children were fed first.