You would say, "What's your ping?" or "What's the ping?" if you are trying to connect to someone in order to play a game online. You would say, "What is ping?" if you didn't understand what the word ping means. Example: Do you want to play a game? - Yes, let's do it. I tried to connect, but I couldn't. What's your ping? - What is ping? Ping is a network query to determine whether there is a connection and how fast it is.

In what context? Both could be correct - the first would need quotes What is 'ping'? That's a more verbal question. The second one would need a specific context, as you are using 'the'. Normally, if you are asking for a meaning, and you don't know if it is a verb or a noun, you would ask. What does 'ping' mean? If you know it is a thing, i.e. a noun, you could also ask 'What is a ping?'

It may depend on the context and on what we are talking about. If the "ping" is referring to a sound, such as an alert sound on a phone, then the correct wording would be "What is the ping?" But if "ping" was the name of something, perhaps a game or a pet, then you could ask "What is Ping?"