Commonly referred to a standard way to see if a network connection is available - a packet is sent to a destination, which returns the packet or additional information.
The gamers definition usually refers to the time it takes for a message to get to and back from a server or another gamer. Usually going through the game's network processing (i.e. the ping is handled by the game and not computer's network hardware or operating system)
The original acronym is from Packet INternet Groper.
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