A put option on a bond is a provision that allows the holder of the bond the right to force the issuer to pay back the principal on the bond. A put option gives the bond holder the ability to receive the principal of the bond whenever they want before maturity for whatever reason. If the bond holder feels that the prospects of the company are weakening, which could lower its ability to pay off its debts, they can simply force the issuerer to repurchase their bond through the put provision. It also could be a situation in which interest rates have risen since the bond was intially purchased, and the bond holder feels that they can get a better return now in other investments.
Another benefit to a bond with this provision is that it removes the pricing risk bond holders face when they attempt to sell the bond into the secondary market, where they may have to sell at a discount. The provision adds an extra layer of security for bond holders - as it gives them a safe exit strategy. Because this option is favorable for bond holders, it will be sold at a premium to a comparable bond without the put provision.
Bonds with a put option are referred to as put bonds or putable bonds. This is the opposite of a call option provision which allows the issuer to redeem all of the outstanding bonds. The exact terms and details of the provision is discussed in the bond indenture.