A put is downside protection. If yields rise or credit deteriorates, the holder can hand the bond back at par instead of riding the price down. That caps the loss and gives the bond positive convexity on the upside in yield.
Because the investor owns the option, a putable bond trades at a lower yield than an identical bullet. Change-of-control puts in high yield indentures are a common variant that protects holders against a leveraged buyout.
Example: a 10-year bond is putable at 100 in year five. Yields rise 150 basis points, taking a comparable bullet to 89. The putable bond holds near 99 because the holder can redeem at par in a year.
Related: callable-bond, convexity, effective-duration, bond-indenture, yield-to-worst