Bitcoin mining is how the bitcoin p2p network gets more bitcoins into circulation.
The p2p network is a distributed SHA-256 calculation and used for transaction tracking.
Every time the hash solves a block, this triggers a transaction of adding more coins to the network. As more blocks get solved, the algorithm gets more complex. Often referred to as the difficulty factor/multiplier.
This can be done using a bitcoin mining client that leverages the computer CPU, computer GPU, FPGA or ASIC. Due to the current and increasing mining difficulty multiplier, strongly recommended against using computer CPU. There will be guides on how to use the variety of popular clients that will help you get started.
Since bitcoins was released to the internet sometime in 2009. There has been a ton of resources that provide in great detail to what bitcoins are and how they work. Please see one of the following sites for more detailed look at bitcoins: