A dad bod is a body optimized for the needs of most men of that age.
Younger guys have chiseled and hard features. Arguably it's the body of a god, like Hercules or something and optimized for most of the activities of the younger guy who has significantly more physical pursuits.
Dad bods are optimized differently. A soft pillow in the mid section designed for children and exhausted spouses. Padding on the body makes it less menacing and more huggable than a washboard or tree trunk. Thicker skin to deal with an influx of certain discussions that begin soon after parenting begins... Still a body of a god, but Buddha instead of Hercules.