The process of mining a new block in the Bitcoin network involves solving a complex mathematical problem using specialized hardware. Miners compete with each other to solve the problem, and the first miner to find the solution gets to add a new block to the blockchain and receive a reward in the form of newly minted bitcoins. The solution to the problem is used to verify transactions in the block and ensure that the block is legitimate. Once the block is added, it becomes a permanent part of the blockchain and is verified by other miners in the network. The process of mining is essential for maintaining the integrity and security of the Bitcoin network, as it helps prevent double-spending and other malicious activities.