Mining
When the Bitcoin cryptocurrency network was designed and set up using Blockchain as the underlying technology, participants had to solve complex mathematical puzzles (or run complex algorithms to come up with an expected outcome) to be allowed to join the network and subsequently participate in executing and approving transactions on the network. A participant that solved the puzzle was awarded some bitcoins as a reward. This process of solving complex puzzles to earn rewards and the rights to validate transactions on the network is referred to as "mining".
The mathematical problem is extremely difficult to solve, but once a valid solution is found, it is easy for the rest of the participants on the network to confirm if the solution is correct. There are multiple possible solutions for any problem, but only one of the solutions needs to be found for the block to be solved.
Blockchain miners need to install and run a special Blockchain mining software that enables their computers to solve the puzzles and communicate securely with one another. As the Blockchain grows, the complexity of mining increases, and so does the computing power required.
The major public cryptocurrency networks today are so large and complex that individuals may not be able to participate as miners as the computing infrastructure required is extremely high in terms of cost and power. The option is to be a part of a consortium that will invest in the required infrastructure and do the mining on behalf of the individuals and proportionately distribute the rewards.
Expensive mining as required for a public cryptocurrency network is not required for private networks since these are networks meant to simplify transactions between participants but not for direct financial gains. For such networks, alternate mechanisms are used to validate transactions.