Bitcoin mining is performed by high-powered computers that solve complex computational math problems; these problems are so complex that they cannot be solved by hand and are complicated enough to tax even incredibly powerful computers.
The result of Bitcoin mining is twofold. First, when computers solve these complex math problems on the Bitcoin network, they produce new Bitcoin. And second, by solving computational math problems, Bitcoin miners make the Bitcoin payment network trustworthy and secure by verifying its transaction information.
When someone sends Bitcoin anywhere, it's called a "transaction". Transactions made in-store or online are documented by banks, point-of-sale systems, and physical receipts. Bitcoin miners achieve the same thing by clumping transactions together in "blocks" and adding them to a public record called the "blockchain". Nodes then maintain records of those blocks so that they can be verified into the future.
When Bitcoin miners add a new block of transactions to the blockchain, part of their job is to make sure that those transactions are accurate. In particular, Bitcoin miners make sure that Bitcoin is not being duplicated, a unique quirk of digital currencies called "double-spending".
Digital information can be reproduced relatively easily, so with Bitcoin and other digital currencies, there is a risk that a spender can make a copy of their Bitcoin and send it to another party while still holding onto the original.
As compensation for their efforts, miners are awarded Bitcoin whenever they add a new block of transactions to the blockchain. The amount of new Bitcoin released with each mined block is called the "block reward". The block reward is halved every 210,000 blocks.(Current block reward in 2020 is 6.25)
This system will continue until around 2140. At that point, miners will be rewarded with fees for processing transactions that network users will pay. These fees ensure that miners still have the incentive to mine and keep the network going. The idea is that competition for these fees will cause them to remain low after halvings are finished.