"Ternary operator" means "operator that takes three things", like unary and binary operators take one and two things.

In C there is an operator for conditional expressions (an 'if' that you can put inside expressions) and it looks like this condition ? trueBranch : falseBranch. It takes three expressions, so it's a ternary operator.

Except it's the only ternary operator in C (and most languages, if they have one at all), so instead of calling it something like "conditional operator", they just call it "the ternary operator"

Honestly, it is not worth it and only mildly funny. You didn’t miss anything.

The joke is that the people in the conversation are kinda dumb

To my deranged Friday afternoon brain, this is the funniest bit