Ok, so I think the story goes like this (I'd be grateful if someone could correct me if I'm wrong). Sorry if this is quite off-topic; I'm trying to get a complete picture of what's going on.
The public deposits money with banks, which they can get back at very short notice.
The banks then lend out most of that money at longer terms, holding only a small percentage of the original depsoits in reserve. It can do this because it's unlikely that large numbers of depositors will want to withdraw most of their deposits at the same time.
If more depositors than expected want their money back, the bank can borrow at short terms from the money markets (ie. other banks) and use the proceeds to pay its depositors. This is what the core reading means when it says that the main players in the money markets are clearing banks who lend and borrow overnight to control their liquidity.
If they are unable to borrow from the money markets, then they can borrow money from the central bank.
The central bank will act as lender of last resort in order to stop an institution going bust because of liquidity problems.
One thing I've also heard discussed is that the government or central bank can buy illiquid assets from banks in order to provide them with cash. The government/central bank can justify doing this because it does not have the same need for liquidity as the clearing banks.
So when we hear about central banks "bailing-out" failing institutions, as we've been hearing in the news, it really means that they are lending them money to help with their liquidity problems. It isn't the government propping-up loss-making institutions, as some recent discussions in the media seem to have implied. The institutions in question are still solvent and can be expected to be profitable.
The current situation has arisen because banks are cagey about lending to each other because of the uncertainty about the quality of the loans that they have made.
Northern Rock for example was more dependant than most banks on short-term borrowing. As I understand it, Northern Rock was not just making longer-term loans out of the money from it's depositors, but also out of short-term loans from other banks. When it became impossible to borrow in this way, it had to go to the central bank for a loan. When depositors got news about this, they started to withdraw money.
Isn't the role of central bank as lender of last resort supposed to stop such things happening - it's intended to make the public confident that the bank will never go under because of lack of liquidity, and so there's no need to rush to withdraw your deposits before the bank goes bust. If the public just sees borrowing from the central bank as a sign of financial weakness that starts a run on the bank, then what's the point of the lender of last resort facility?
A major liquidity crisis such as this one can cause solvency issues for some - for example - interest rates go up, borrowers default, house-prices crash and some are made insolvent by this reduction in the value of their assets.
Another example I heard was that certain institutions were selling huge quantities of less liquid assets to convert them to cash or more liquid assets - thus reducing the value of the less liquid assets and causing insolvencies for similar reasons.
Sorry this is a long post. I hope it's helpful and I'd be grateful if someone could let me know if I've got anything wrong.
Thanks,
Sam