Volatility makes that requirement go up because of the time risk. If you agree to buy something for $300, fail to settle, and it drops to $20 in the meantime that counterparty is out more money.
The amount of money they are required to keep on hand varies according to the risk of the investment (among other things). The increased volatility translates into higher risk and therefore requires the broker to keep more money on hand.
I haven't seen the exact amount in this case other than hearing total amount of $14 billion and that it would be a percentage of that.
Edit: nrmitchi below explained how the broker is legally required to have some extra collateral on hand in between accepting and clearing the order.
The answer is that even cash-settled trades take 2 days to settle, which most traders would consider an unacceptable wait to take delivery of their shares in this day and age. Seeing the shares appear in your account immediately after buying is merely an abstraction provided by brokers, and the brokers need to have their own cash on deposit to secure this.
BTW a few years ago, it was T+3.
Yes, if Robinhood is letting people trade on margin, then Robinhood needs to have the cash to support that margin. That is one thing. And they have largely, as far as I know, disabled that already.
The other part is that they are required to have reserves and collateral for trades that are "cash" until they settle, as all brokerages are. I am not an expert here, but my understanding is that this requirement increases as volatility goes up, as as correlation of trades goes up (ie, if all of the volume is in a couple stocks, it's highly correlated, and thus the reserve requirement is higher). This must be, by regulation, Robinhood's money (ie, not customer funds), and Robinhood just didn't have the money to keep opening new positions.
As for the underlying why of the requirement, I don't know. I assume it has something to do with preventing brokerages from accepting increasingly risk trades during high volatility events (which, ya, is what's happening right now). But either way, it's the current rule, and as a brokerage, they have to follow it.