Back in the 1960s, a Greek banker in London[1] wanted to find a way for banks to make syndicated floating-rate loans. He found a very simple answer: The banks would lend money to a company, charging their cost of funds plus a spread, and every three months, you'd go out and ask the banks what their cost of funds was, and you'd average their answers, and that (plus the fixed spread) would be the new interest rate on the loan. This was a simple product for the banks: They could pass their costs on directly to the customer, and make a fixed profit (the spread). And by surveying all the big banks and throwing out outlier submissions, you could get a pretty fair approximation of the overall funding cost for banks.
And so this -- Libor, the London interbank offered rate -- became the normal way that everyone did floating-rate loans, and then it became the normal way that everyone did interest-rate derivatives, and then it became the normal way that everyone did ... sort of ... everything? Libor just sort of became The Interest Rate, used for discounting cash flows in all sorts of transactions, "the most important number in the world." But it was always based on a survey of banks' funding costs, and so it was always a little hazy. One problem was that the banks could lie. But a second problem is that the banks might not even know. Libor surveys asked banks each day what they would have to pay to borrow money unsecured from other big banks, but over time the banks sort of stopped doing that, particularly in some of the more obscure combinations of tenors and currencies that nonetheless reported Libor rates. So the banks' Libor submitters would guesstimate their submissions based on deposit rates and commercial-paper rates and secured-borrowing rates and other tenors and what brokers and their buddies were telling them. It was all more or less good enough as a casual system for resetting the rates on a few billion dollars worth of syndicated loans, but it was not accurate down to the hundredth of a basis point as a foundation for the financial system, or as the source for pricing hundreds of trillions of dollars of derivatives.
[1] Minos Zombanakis: https://www.bloomberg.com/news/features/2016-11-29/the-man-w...