That constraint is what makes the problem more or less difficult. More leading zeroes means fewer possible solutions, and more time required to solve the problem. Every 2,016 blocks (roughly two weeks), that difficulty is reset. If it took miners less than 10 minutes on average to solve those 2,016 blocks, then the difficulty is automatically increased. If it took longer, then the difficulty is decreased.
Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented by an unknown person or group of people using the name Satoshi Nakamoto and released as open-source software in 2009. Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies, products, and services. Research produced by the University of Cambridge estimates that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.