To cuddle is to embrace in a loving, affectionate way. If you're having a terrible day, you probably wish you could just go home, get in bed, and cuddle with your cat.
Cuddle might come from the Middle English couth, "known" — after all, you only cuddle with those you know. Or, cuddle may have started as baby talk that caught on. When you cuddle, you give a snuggly hug to make yourself or another person feel loved or comforted. As a noun, cuddle describes the time of the embrace, like having one last cuddle before leaving for a long trip.