(paraphrasing from Twitter) It means they have to let the mafia pull out their money first so that no one ends up murdered. Then they'll let the normal folks withdraw.
One possible example: their usual transactions to fill up the hot wallet are not going through because too low fees, or timelocks/multi sig issues, and now unexpectedly they need to go to the cold wallet and this takes time.
I bet they are doing waay more withdrawals today, many times over their usual volume so they are hitting some capacity issues, and you can't rush these things.
What they probably mean is that they have a transaction that consumes $1000000 on their address and creates two outputs: $100 withdrawal for client A, and $999900 on a "change" output. Later withdrawals have to link to that change output (bitcoin is a directed acyclic graph of inputs-outputs). If that transaction is not confirmed, then later txs also cannot be confirmed and backlog grows.