Here's an answer short on math, as requested.
First, understand the "risk-free bond" part:
Let's assume there's a magical company that always has a 100% chance of paying their debts, no matter what. Because our magical company has 0% chance of default, lending to them would be identical to a risk-free bond.
Of course, there's no such thing as a company that has no risk.
So to make this a realistic company, the Merton model adds a 'risk component' to that risk-free bond.
That's where the "short put" comes in.
In our "realistic" company, the bond holders have a zero-coupon bond with a par value equal to the company's debt. If this company's assets drop below the value of its debt, the bond holders obviously get less than par value. The most they can get is the total asset value of the company in that case.
Mathematically, for bond holders that's the same thing being short a put option. Why? Because the bond holders don't lose anything if the company's assets are valued higher than its debts. But the bond holders do lose if the assets fall below the value of its debt.