The bitcoin network is secured by the distributed network of computers all around the world that are running the bitcoin program through a process called "proof of work."
People that run the bitcoin software to secure the network are called "bitcoin miners." Miners are cryptographically securing the network by ensuring that coins are not counterfeited and that the network runs smoothly.
Bitcoin miners are incentivized for securing the network by being rewarded with newly "minted" bitcoin proportional to the computational power they contributed to the network.
You can think of proof of work like an impenetrable wall of computational power that one would need to overcome to cheat the network.
Proof of work ensures that any changes to the history of the network are incredibly difficult (and expensive!) to make.
Making a change just three blocks back, for example, makes it three times as difficult to alter the history of the network in any way. For someone to cheat the network, it becomes exponentially more difficult over time. Anyone trying to change the network also falls behind other miners.
Just how difficult is it? The sequence pictured below is currently executed over 120 quintillion times every second by miners!
Bitcoin nodes then verify the validity of each new block.
The miners then "settle" those transactions on the network.