The situation in the banks is similar: there are collateral requirements that have to be met, trades with other banks that have to be honored, etc. A bank can cover its day-to-day operational expenses and be cash-flow positive, but if it suddenly has to pay someone else a big chunk of money that it doesn't have the liquid assets to provide, then it's still insolvent.
Say that you take out a mortgage on a new house. The bank lets you borrow up to a certain percentage of the house's value, say 90%. The other 10% is a down payment that you must meet with your own money.
Now lets say the value of your house falls from $100,000 to $90,000. The way your mortgage is written, you probably still owe the bank $90,000 (90% of the original purchase price). However, the way debt contracts are written in the financial world, you would have to PAY the bank $9,000 to reduce your total borrowing to 90% of the CURRENT value of the property, or $81,000. That $9,000 payment is a "margin call" in financial market terminology.
So, financial firms borrow up to a certain amount of the assets that they lend, say 90%. If the value of those assets drops in half, and the value of mortgages plummeted on the open market, they owe their lenders enormous sums (45% of the value of the assets, for a 50% drop in value on 90% leverage).
Those margin calls forced a lot of firms out of business, even though their assets were still performing and still paying enough to meet their debt payments and operating expenses. If the firms could call their mortgages, they would be fine, but they can't because the mortgage money is spent on a house which is a non-liquid asset. The financial firms likely thought that their assets were undervalued on the market because of the panic that set in, but no matter. That's not the way their contracts were written.