Maturity transformation is when banks take short-term sources of finance, such as deposits from savers, and turn them into long-term borrowings, such as mortgages.
Despite all the furore that's surrounded the sector recently, retail banks perform a vital role in an economy. They take short-term sources of finance, such as deposits from savers and money market loans, and turn them into long-term borrowings, such as mortgages.
This is called maturity transformation a rather grand way of saying that they exist to meet the needs of lenders and borrowers. In return for providing this service they make money by charging more for a loan than they offer to pay on, say, a deposit.
However, this process can backfire. For example, if there is a panic and a bank run, savers may all try to withdraw money at once. Equally, the money markets may suddenly dry up as lenders stop providing short-term loans to each other. Northern Rock demonstrated what can go wrong here just before it was bailed out by the government.