In the case of Bitcoin, this process is not done by individuals or companies, but by thousands of computers around the world that connect to the internet. These computers are known as miners or 'miners'. Simply put, they are 'computers that process transactions'.
To perform this processing in a secure way, the computers need to do complex calculations that make up enormous computing efforts, so it takes great energy and sophisticated special tools as well. Someone - the owner of these computers - needs to pay for these tools and electricity, so they have to get compensation from all the effort and money they spend to support this network. They get compensated through the newly mined Bitcoin. The mined new bitcoin acts as a reward and incentive for those who contribute to systems that support the transaction process.
Another way to understand this is to imagine what happens if big banks build the world's largest global transaction processing system: they'll spend billions of dollars and charge a small transaction fee to users to cover the cost of building the system.
With Bitcoin mining, the cost for this global system is divided into thousands of computers, and they cover their costs with the newly mined Bitcoin. Long story short, this is the democratization of financial infrastructure.