The "one bite" rule says that if any domestic animal (a dog or any other domestic animal) has a propensity to do something unusual for its class (such as biting people or knocking them down), and that unusual thing is something that causes harm to person or property, and the owner of the animal is aware of all of this, then the owner, harborer or keeper of the dog will be held legally liable if the animal does that same thing, and it causes harm.
When it comes to dogs, therefore, the test is whether the dog previously showed a desire to bite a person (i.e., a vicious temperament), or to play too hard which can knock down a person (i.e., dangerous behavior). Note that the term "one bite" is a misnomer because an actual bite is not required by the rule.
If a dog never showed any sign of being vicious, and then it mauls someone, the owner, harborer or keeper probably will NOT be held legally liable and will NOT be convicted of a crime because of the lack of knowledge that the harm could occur. This is why there was a not guilty verdict in the child cruelty case of Marco Zamudio Jr, 23, following the brutal, fatal mauling of his nephew last year.
On the other hand, if the dog acted aggressively toward people but NEVER bit anyone, the owner, harborer or keeper can be convicted of crimes up to second degree murder, as was the case of Marjorie Knoller, convicted of second degree murder following the fatal mauling of Diane Whipple in 2001. See The Diane Whipple Case.
The one bite rule is the basic legal ground for legal liability, both civil and criminal. However, it is NOT the ONLY legal ground. Among other things, a dog bite victim in almost every state can base a claim on negligence or violation of an animal control law cauing injury. In two-thirds of the states, there are dog bite statutes that eliminate the one bite rule's requirement that the dog previously acted vicious or dangerous. These statutes sometimes cover all injuries (not just bites), and all custodians of the dog (not just the owners). For more, see Legal Rights of Dog Bite Victims in the USA.
For more about the one bite rule, see Overview of the One Bite Rule.