So what in the heck does all this mean?
I could just redirect you to the wikipedia article (http://en.wikipedia.org/wiki/LIBOR), which begins as follow:
"The London Interbank Offered Rate (or LIBOR, pronounced /ˈlaɪbɔr/) is a daily reference rate based on the interest rates at which banks offer to lend unsecured funds to other banks in the London wholesale money market (or interbank market)."
But let's break it down. First off, note that LIBOR is an acronym--London InterBank Offered Rate. Let's break that down letter by letter:
R for Rate: LIBOR is an interest rate, just like a mortgage rate or an interest rate on a CD you've got with a bank. With a mortgage rate, you've borrowed money, and you're paying that interest rate on the principal to whoever holds the mortgage (as we've learned over the past few months, that could in fact be holders of mortgage-backed securities all over the world, but let's not get into that now). With a CD, you've actually loaned your money to the bank, and they're paying you the interest rate on the amount you've invested (lent).
So who are the borrowers and lenders when it comes to LIBOR? It's an InterBank rate--it's an interest rate for interbank lending, i.e., for loans between banks. Why do banks lend to each other? Let's not get into that right now either.
What do we have left? An L and an O: L for London is something of an historical artifact--that the rate is set by the London wholesale money markets, i.e., the interbank lending market in London, b/c the British Banker's Association took the initiative to do so in 1984, and it subsequently became the benchmark rate for all kinds of finance-related stuff all over the world.
O for Offered means, as the wikipedia quote says, a measure of the rate at which banks *offer* to lend to the other banks. There is also LIBID, which is a bid rate instead of an offer rate--a measure of the rate at which banks are accepting deposits from other banks.
Why is it so important? LIBOR is a measure of banks' "cost of capital"--how much it costs them to raise funds to do business, or conversely how much they can earn on their excess cash. And it's also a measure of how much they trust that their fellow banks (their counterparties) will be able to repay these loans--when LIBOR spikes, as it has over the past month, it means that banks are very reluctant to lend to each other. It's clear why that is these days--banks are worried that any given bank that they lend to may not be around to repay the loan when it comes due (cf. Lehman, Bear, etc.)
That raises another point--how long are these loans for (more precisely, what is their maturity). There are actually multiple LIBOR rates--the most common ones are overnight, 1 month, 3 month, 6 month and 1 year. Currently bank are very reluctant to lend beyond the overnight maturity--they're worried about what could happen in the next month, the next 3 months, etc.
I'll close with one more reason why LIBOR is important, which is a bit more wonky. A striking feature of the Black-Scholes option pricing formula (that's for another day--see http://en.wikipedia.org/wiki/Black-Scholes) is that the interest rate that appears in it is the "risk-free rate," which is the rate at which the market participant can borrow and lend with no risk (of default). Sometimes this is assumed to be the US Treasury rate, but often banks who trade in derivatives markets use LIBOR as a proxy for the risk-free rate (see for example Section 4.1 of Hull, http://www.amazon.com/Options-Futures-Other-Derivatives-5th/dp/0130090565).
Hence, with LIBOR so crazy and volatile, trading desks have difficulty pricing and hedging their derivatives books..
Finally, here is the BBA's website, which has much more on LIBOR, including historical data: http://www.bba.org.uk/public/libor/
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