LIBOR stands for London Inter Bank Offered Rate. It's the rate of interest at which banks offer to lend money to one another in the so-called wholesale money markets in the City of London. Money can be borrowed overnight or for a period of in excess of five years.
The most often quoted rate is for three month money. '3 month LIBOR' tends to be used as a yardstick for lenders involved in high value transactions. They tend to quote rates as 'points above LIBOR'. So if 3 month LIBOR were (say) six per cent, a bank may choose to lend to another bank at (say) 6 and a quarter per cent. e.g. a quarter per cent above above 3 month LIBOR.
Lending to individuals tends to be based on base rates which are set by the Chancellor after consulting with the Bank of England. Base rates tend to be less volatile. Some home lenders offer mortgage rates linked to LIBOR. The lender offers funds in Sterling or in a foreign currency. Bear in mind that LIBOR-linked borrowing by individuals is higher risk, especially if you are borrowing in a foreign currency.
The LIBOR rates are set each day at 11am by leading banks but rates fluctuate throughtout the trading session according to sentiment about the outlook for base interest rates. LIBOR rates are listed each morning in the Financial Times and other newspapers.
Banks also offer to borrow money in the wholesale money markets. The rate is called the London Inter Bank Bid Rate (LIBID).