In law*, battery is a tort, consisting of a physical touching without consent, justification or privilege.
While the term "battery" originally referred to a beating, it has evolved into a question of consent rather than a matter of violence. Under the modern definition of "battery", if a surgeon operated without the patient's consent it could be deemed a "battery", whereas a thorough beating in the course of sporting event would not, as long as it was administered within the rules of the game. (Thus, in American football, a properly executed tackle could not be a "battery", but clipping might be, because it is against the rules.)
Privilege enters in when someone has a legal right to push you around. A shopkeeper, for example, can revoke your permission to be in his store and physically remove you from the premises. If a shopkeeper's goons beat the crap out of you, it would still not be a "battery" (though you might sue for "excessive use of force", which is a kind of negligence).
"Battery" is seldom asserted without a complementary claim of "assault", but they are distinct ideas in tort law. "Assault" consists of threatening bodily harm: it doesn't require actually carrying out the threat.
In criminal law, "assault" and "battery" are used somewhat interchangeably, or together, usually for violent attacks that actually do some serious damage.
*In Anglo-American civil
common law, that is.