An exploding offer is simply one that has a deadline set so short that the recipient must accept or reject on the spot.
In startup funding, they're intended to prevent you from comparing an offer to other potential offers from other investors. In the Airbnb case, they're intended to prevent you from consulting with a lawyer or further appraising your damages.
I'd call it a poison pill. Consider what it most likely is trying to prevent you from doing, and then go do that instead of what condition the poison pill is attached to.
"Poison pill" has a very different, established meaning in corp law. "Exploding" here hews well to the old Mission Impossible bit: "This message will self-destruct in ten seconds."
I don't object to you calling it that, but it is literally the thing people are talking about when they refer to "exploding offers" from venture capitalists, which is the irony here.
In startup funding, they're intended to prevent you from comparing an offer to other potential offers from other investors. In the Airbnb case, they're intended to prevent you from consulting with a lawyer or further appraising your damages.